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APTITUDE TEST 1

TOTAL QUESTIONS = 20

TOTAL TIME = 30min

Mother’s age when Ayesha’s brother was born = 36 years.

Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years.

Required difference = (42 – 36) years = 6 years

1 / 20

Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents..?

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)

Odd days in 1600 years = 0

Odd days in 300 years = (5 x 3)  1

97 years has 24 leap years + 73 ordinary years.

Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.

Jan.  Feb.   March    April    May      June (31 +  28  +  31   +   30   +   31   +   17) = 168 days

168 days = 24 weeks = 0 odd day.

Total number of odd days = (0 + 1 + 2 + 0) = 3.

Given day is Wednesday.

2 / 20

What was the day of the week on 17th June, 1998

LOGARITHMS’ contains 10 different letters.

Required number of words= Number of arrangements of 10 letters, taking 4 at a time.
10P4
= (10 x 9 x 8 x 7)
= 5040

3 / 20

How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed..?

Since the month begins with a Sunday, to there will be five Sundays in the month.

Required average
=510 x 5 + 240 x 25
30
=8550
30
= 285

4 / 20

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is

Let ten’s and unit’s digits be 2x and x resprctively.

Then, (10 x 2x + x) – (10x + 2x) = 36

  • 9x = 36
  • X =4

Required difference = (2x + x) – (2x- x) = 2x= 8

5 / 20

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2..?

6 / 20

A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is..?

 

7 / 20

Choose the Number which is different from other

196, 169, 144, 121, 100, 80, 64

Number of ways of selecting 3 consonants from 7
7C3
Number of ways of selecting 2 vowels from 4
4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
= (7C3 × 4C2)=210
It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves

8 / 20

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed..?

Greatest number of 4-digits is 9999.

L.C.M. of 15, 25, 40 and 75 is 600.

On dividing 9999 by 600, the remainder is 399.

 Required number (9999 – 399) = 9600

9 / 20

The greatest number of four digits which is divisible by 15, 25, 40 and 75 is

Suppose B joined for x months. Then,

Then,85000 x 12=3
42500 x x1
      

 

 x =85000 x 12= 8.
42500 x 3

So, B joined for 8 months

10 / 20

A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1..?

Largest 4-digit number = 9999

 

88) 9999 (113

88

—-

119

88

—-

319

264

55

 

Required number = (9999 – 55)

= 9944

11 / 20

The largest 4 digit number exactly divisible by 88 is

Clearly, l = (48 – 16)m = 32 m,

b = (36 -16)m = 20 m,

h = 8 m.

 Volume of the box = (32 x 20 x 8) m3 = 5120 m3

12 / 20

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is.

B’s 10 day’s work =1x 10=2.
153

 

Remaining work =1 –2=1.
33

 

Now,1work is done by A in 1 day.
18

 

1work is done by A in18 x1= 6 days.
33

 

 

13 / 20

A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work..?

14 / 20

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is..

Let their marks be (x + 9) and x.

Then, x + 9 =56(x + 9 + x)
100

25(x + 9) = 14(2x + 9)

3x = 99

x = 33

So, their marks are 42 and 33

15 / 20

Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are.

Let C = x. Then A = (x—20) and B = (x—40).
x + x – 20 + x – 40 = 120 Or x=60.
A:B:C = 40:20:60 = 2:1 :3.
B’s share = Rs. 120*(1/6) = Rs. 20

16 / 20

Rs. 120 are divided among A, B, C such that A’s share is Rs. 20 more than B’s and Rs. 20 less than C’s. What is B’s share..?

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o’clock).

AM

12:00   1:05    2:11    3:16
4:22     5:27    6:33    7:38
8:44     9:49    10:55

17 / 20

How many times do the hands of a clock coincide in a day..?

18 / 20

Reena and Shaloo are partners in a business. Reena invests Rs. 35,000 for 8 months and Shaloo invests Rs. 42,000 for 10 months. Out of a profit of Rs. 31,570, Reena’s share is:

C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.

S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.

 Gain =80x 100% = 5%.
1600

19 / 20

A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is

20 / 20

 At what time between 7 and 8 o’clock will the hands of a clock be in the same straight line but, not together?

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APTITUDE TEST 2

TOTAL QUESTIONS = 20

TOTAL TIME = 30min

Ratio of the profits = 25000*12 : 60000*8
= 25*12 : 60*8 = 5*3 : 12:2 = 5 : 4*2
= 5:8
Let the total profit = x.
Then Kamal received `(10x)/100 = x/10` as commission for managing the business
Remaining profit = `x- x/10 = (9x)/10` which is shared in the ration 5:8
Kamal’s share = `x/10 + ((9x)/10) * (5/13) = 58000`
=> `x + 9x(5/13) = 580000`
=> `x(1 + 45/13) = 580000`
=> `x ( 58/13) = 580000`
=> `x ( 1/13) = 10000`
=> `x = 130000`
Kiran’s share = 130000 – 58000 = 72000

1 / 20

Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive..?

Average speed = total distance / total time

Total distance covered = 6 miles; total time = 45 minutes = 0.75 hours

Average speed = 6/ 0.75 = 8 miles/hour

2 / 20

Jack takes 20 minutes to jog around the race course one time, and 25 minutes to jog around a second time. What is his average speed in miles per hour for the whole jog if the course is 3 miles long..?

= `((8.77)^3 + (4.23)^3) / ((8.77)^2 – (8.77 xx 4.23)+ (4.23)^2)`

   = `(a^3 + b^3)/ (a^2 – ab+ b^2)`

   = `(a+b)`

   = `8.77+4.23 `

   = `13`

3 / 20

Find the product of

`(8.77 x 8.77 x 8.77+ 4.23 x 4.23 x 4.23)/(8.77 x 8.77 – 8.77 x 4.23+ 4.23 x 4.23)`

The difference between the length and breadth is = 23 m.

i.e., (l – b) = 23——– eq.(1)

And perimeter = 206 m.

i.e., 2(l + b) = 206

       l + b = 103———eq.(2)

By solving eq.(1) and (2), we get length(l) = 63 and breadth(b) = 40.

So, Area = ( l x b ) = (63 x 40) m2 = 2520 m2.

4 / 20

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area in m2 is..?

B received 2/3 of the profit
=> A : B = `1/3 : 2/3 = 1:2`
Let the total capital = x
Then A’s capital = `x/4`
B’s capital = `x – x/4 = (3x)/4`
Assume B’s money was used for b months
Then A:B = `(x/4)**15 : ((3x)/4)**b = 1 : 2`
=> `15/4 : (3b)/4 = 1 : 2`
=> `15 : 3b = 1 : 2`
=> `5 : b = 1 : 2`
=> `5/b = 1/ 2`
=> `b = 5**2 = 10`

5 / 20

A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B’s money was used ..?

C.P for shopkeeper = Rs.200

Required Profit % = 20%

=> Required Total S.P = 1.2 * 200 = Rs. 240

Toffees Left = 100 – 10 = 90

S.P for Each Toffee = 240/90 = Rs. 2.67

6 / 20

A shopkeeper bought a box of 100 toffees for Rs. 200. His son ate 10 toffees (ofcourse, without paying!). At what S.P should each toffee be sold so shopkeeper makes an overall profit of 20%…?

The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time= `”8.5km”/”0.5 kmph” = 17 hrs

7 / 20

Two monkeys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction..?

573 is not a perfect square

8 / 20

Find the odd man out:
4, 9, 256, 529, 573

There are 12 months in a year. Hence, 180 months is 15 years. If the person’s current age is 28 years, then his age after 15 years would be 43 years which is the required answer.

9 / 20

What would be the person’s age after 180 months if his current age is 28 years..?

Sum of present ages of A, B and C is = 92 years

Therefore , Sum of their ages 4 years ago = 92 – (4 * 3)= 80 years.

4 years ago ratio of the ages of A , B and C was = 1:2:3

Therefore, A’s age four years ago = `1/6` * 80 = 13.3 years.

So , A’s present age =13.3 + 4 = 17.3 years

10 / 20

Sum of present ages of A, B and C is 92 years. If 4 years ago, the ratio of their ages were 1:2:3 respectively, find A’s present age

Let the total profit be Rs. 100.

After paying to charity, A’s share  =  = Rs. 57.

If A’s share is Rs. 57, total profit = Rs. 100.

If A’s share is Rs. 855, total profit  =  = 1500.

11 / 20

A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A’s share is Rs. 855, the total profit is..?

Total distance = 39 km
Total time = 45 min
D = S*T
`x * 15/60 + 2x * 20/60 + x * 10/60 = 39 km `
x = 36 kmph

12 / 20

A motorist covers a distance of 39km in 45min by moving at a speed of x kmph for the first 15min, then moving at double the speed for the next 20 min, and then again moving at his original speed for the rest of the journey. Find x..?

Total distance = 39 km
Total time = 45 min
D = S*T
`x * 15/60 + 2x * 20/60 + x * 10/60 = 39 km `
x = 36 kmph

13 / 20

A motorist covers a distance of 39km in 45min by moving at a speed of x kmph for the first 15min, then moving at double the speed for the next 20 min, and then again moving at his original speed for the rest of the journey. Find x..?

Let speed of the train be x km/hr and of the car be y km/hr.

Then, `120/x + 480/y = 8`

=> `1/x + 4/y = 1/5`    — (i)

And, `200/x + 400/y = 25/3`

=> `1/x + 2/y = 1/24`    — (ii)

Solving (i) and (ii), we get x = 60 and y = 80.

Ratio of speeds = 60: 80 = 3:4

14 / 20

If 120 km is done by train and the rest by car, then it takes 8 hours for a 600 km journey. Of 200 km is done by train and the rest by car, then it takes 20 minutes more. Then what would be the ratio of the speed of the train to that of the car..?

Clearly, we have : length(l) = 9 ft.

and l+2b = 37 ft.

i.e., 9+2b = 37 

       2b = 37-9

       2b = 28

       So, the breadth(b) = 14 ft.

Area = (l x b) = (9 x 14) sq.ft. =126 sq.ft.

15 / 20

A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet..?

Let the average age of the team is x years.

11x – (26+29) = 9(x-1)

x = 23

16 / 20

The captain of a cricket team of 11 players is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded the average age of remaining players is one year less than the average age whole team. What is the average age of the team…?

Sum of Alternate number gives next alternate number.

1+2=3;2+3=5;3+5=8;

1+3=4;3+4=7;

7 is the correct number in sequence not 9

17 / 20

Find the odd number:

1,1,2,3,3,4,5,9,8

  Let the edge = `a` cm 

So increase by `50%` = `a+a/2 = 3a/2`

Total surface Area of original cube = `6a^2`

TSA of new cube = `6(3a/2)^2`

`6 x 9a^2/4 = 13.5a^2`

Increase in area = `13.5a^2 – 6a^2 = 7.5a^2`

 `7.5a^2` Increase % = `(7.5a^2)/(6a^2) xx 100 = 125%`

18 / 20

If each edge of a cube is increased by 50%, find the percentage increase in its surface area…?

28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)

We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)

Number of odd days in the period 2001-2005
= 4 normal years + 1 leap year
= 4 x 1 + 1 x 2 = 6

Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148

148 days = 21 weeks + 1 day = 1 odd day

Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday

Hence May 28 2006 is Sunday

19 / 20

What day of the week does May 28 2006 fall on..?

Total distance = 39 km
Total time = 45 min
D = S*T
`x * 15/60 + 2x * 20/60 + x * 10/60 = 39 km `
x = 36 kmph

20 / 20

A motorist covers a distance of 39km in 45min by moving at a speed of x kmph for the first 15min, then moving at double the speed for the next 20 min, and then again moving at his original speed for the rest of the journey. Find x..?

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APTITUDE TEST 3

TOTAL QUESTIONS = 30

TOTAL TIME = 45min

Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 x 10 = 320.
Now increase in avg = 4runs. So, new avg = 32+4 = 36runs
Total runs = new avg x new no. of innings = 36 x 11 = 396
Runs made in the 11th inning = 396 – 320 = 76

1 / 30

The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4..?

Let each side of the square be a. Then, area = a2.
New side =(125a/100) =(5a/4). New area = (5a/4)2 =(25a2)/16.
Increase in area = ((25 a2)/16)-a2 =(9a2)/16.
Increase% = [((9a2)/16)×(1/a2)×100] % = 56.25%.

2 / 30

If each side of a square is increased by 25%, find the percentage change in its area..?

Required number = (L.C.M. of 12, 15, 20, 54) + 8 = 540 + 8 = 548

3 / 30

 The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is…?

4 / 30

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is..

After charity, 90% of the profit is to be divided in the ratio 4:5.
Let total profit is x
Neha’s share is 4/9 of 90%x
So 4/9 of .9x = 1900
x = 1900 x9/.9 x4 = Rs.4750

5 / 30

Neha & Megha invests in a partnership business in the ratio 4:5. If share of Neha is Rs. 1900 and also 10% of profit goes to charity. Find the total profit..?

Clearly, we have : length(l) = 9 ft.

and l+2b = 37 ft.

i.e., 9+2b = 37 

       2b = 37-9

       2b = 28

       So, the breadth(b) = 14 ft.

Area = (l x b) = (9 x 14) sq.ft. =126 sq.ft.

6 / 30

A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet..?

Let C = x. Then A = (x—20) and B = (x—40).
x + x – 20 + x – 40 = 120 Or x=60.
A:B:C = 40:20:60 = 2:1 :3.
B’s share = Rs. 120*(1/6) = Rs. 20

7 / 30

Rs. 120 are divided among A, B, C such that A’s share is Rs. 20 more than B’s and Rs. 20 less than C’s. What is B’s share..?

Probability of drawing 1 blue pen = 4/9
Probability of drawing another blue pen = 3/8
Probability of drawing 1 black pen = 3/7
Probability of drawing 2 blue pens and 1 black pen = 4/9 * 3/8 * 3/7 = 1/14

8 / 30

 A pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, NOT replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen..?

Amount = Rs. (30000 + 4347) = Rs. 34347
Let the time be n years.
Then, 30000(1 +7n/100)= 34347
(107/100)^ n=34347/30000=11449/10000= (107/100)^2
n = 2 years

9 / 30

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is…?

10 / 30

Choose the Number which is different from other

196, 169, 144, 121, 100, 80, 64

11 / 30

How many signals can be made using 6 different coloured flags when any number of them can be hoisted at a time..?

Let the number of 20 paise coins be x. Then the no of 25 paise coins = (324 – x).
0.20 * (x) + 0.25 (324 – x) = 71 => x = 200.

12 / 30

The total of 324 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is..?

Speed = (54 * 5/18) m/sec = 15 m/sec

Length of the train = (15 x 20) m = 300 m.

Let the length of the platform be x meters.

then, x+300 / 36 =15

x+300 = 540

x = 240m

13 / 30

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform..?

Ratio of the profits = 25000*12 : 60000*8
= 25*12 : 60*8 = 5*3 : 12:2 = 5 : 4*2
= 5:8
Let the total profit = x.
Then Kamal received `(10x)/100 = x/10` as commission for managing the business
Remaining profit = `x- x/10 = (9x)/10` which is shared in the ration 5:8
Kamal’s share = `x/10 + ((9x)/10) * (5/13) = 58000`
=> `x + 9x(5/13) = 580000`
=> `x(1 + 45/13) = 580000`
=> `x ( 58/13) = 580000`
=> `x ( 1/13) = 10000`
=> `x = 130000`
Kiran’s share = 130000 – 58000 = 72000

14 / 30

Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive..?

(L – x12)x23 = L(x13 – x12)= (400 – 20)x23 = 400(39 – 20)= x23 = 20 metres

15 / 30

A can give B a start of 20 metres and C a start of 39 metres in a walking race of 400 metres. How much can B give C a start…?

The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time= `”8.5km”/”0.5 kmph” = 17 hrs

16 / 30

Two monkeys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction..?

In the same time, they cover 110 km and 90 km respectively.

For the same time, speed and distance is inversely proportional.

So ratio of their speed = 110:90 = 11: 9

17 / 30

 Two trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds..?

Pattern is 1 * 2, 2 * 3, 3 * 4, 4 * 5, 5 * 6, 6 * 7, 7 * 8

i.e) 8 * 9 = 72

18 / 30

Find the Missing Number 2, 6, 12, 20, 30, 42, 56, __

Let the costs of each kg of apples and each kg of rice be Rs.a and Rs.r respectively.
10a = 24r and 6 * 20.50 = 2r
a = 12/5 r and r = 61.5
a = 147.6
Required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5
= 590.4 + 184.5 + 102.5 = Rs.877.40

19 / 30

The cost of 10 kg of apples is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is Rs.20.50. Find the
total cost of 4 kg of apples, 3 kg of rice and 5 kg of flour..?

L.C.M. of 2, 4, 6, 8, 10, 12 is 120. So, the bells will toll together after every 120 seconds(2 minutes). In 30 minutes, they will toll together30 + 1 = 16 times.

20 / 30

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together..?

Total distance = 39 km
Total time = 45 min
D = S*T
`x * 15/60 + 2x * 20/60 + x * 10/60 = 39 km `
x = 36 kmph

21 / 30

A motorist covers a distance of 39km in 45min by moving at a speed of x kmph for the first 15min, then moving at double the speed for the next 20 min, and then again moving at his original speed for the rest of the journey. Find x..?

2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days

22 / 30

A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it…?

Let Rahul’s age be x years. Then, Sachin’s age = (x-7) years.
x-7 / x = 7 / 9 <=> 9x – 63 = 7x <=> 2x = 63 <=> x = 31.5.
Hence, Sachin’s age = ( x – 7 ) = 24.5 years

23 / 30

Sachin is younger than rahul by 4 years. If their ages are in the respective ratio of 7:9, how old is Sachin..?

12 is an even number. All other given numbers are odd

24 / 30

Find the no which is different from other

1, 3, 9, 12, 19, 29

Work done by leak in 1 hour = (1/8 – 1/10) = 1/40
The leak will empty the cistern in 40 hours.

25 / 30

 A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in..?

D = 32 – 4 ⋅ 4 = -7 < 0
So the equation has 0 real roots

26 / 30

How many real roots does the equation have?  x2+3x+4=0….

Cost of 1 litre of water = Rs.0 = cheaper quantity.
Cost of 1 litre of juice = Rs.24 = dearer quantity.
And, the mean price = m = Rs.20
Therefore, (Cheaper quantity) : (Dearer quantity) = (d – m) : (m – c) = 4:20 = 1:5
Hence, the required answer is 1:5

27 / 30

 In what ratio,water must be mixed with fruit juice costing Rs.24 per litre so that the juice would be worth of Rs.20 per litre..?

Required area =area of the semicircle –area of the right-angled triangle
So 1/2 *22/7*7*7-1/2 *7*7=77-49=28 sq cm

28 / 30

 A right angled isosceles triangle is inscribed in a semicircle of radius 7 cm . The area enclosed by the semicircle but exterior to the triangle is A right angled isosceles triangle is inscribed in a semicircle of radius 7 cm . The area enclosed by the semicircle but exterior to the triangle is..?

Part filled in 4 minutes =4(1/15+1/20) = 7/15
Remaining part =(1-7/15) = 8/15
Part filled by B in 1 minute =1/20 : 8/15 :: 1:x
x = (8/15*1*20) = 1023min = 10min 40sec
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec

29 / 30

Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank..?

Let us name the trains as A and B. Then,

(A’s speed) : (B’s speed) = b : a = ⩗16 : ⩗9 = 4 : 3.

30 / 30

Two, trains, one from Ranchi to Patna and the other from Patna to Ranchi, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is

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APTITUDE TEST 4

TOTAL QUESTIONS = 30

TOTAL TIME = 45min

let the no of bottles be ‘B’.Using chain rule:
(6*1)/270 =(10*4)/B => B = 1800

1 / 30

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes..?

H = 5, L = 2B, Area of 4 = Area of wall paper
2(LH) + 2(BH) = 240 × 50/100
10L + 10 B = 24 × 5, 10L + 5L= 24 × 5
15 L = 24 × 5, L =24×5/15 = 8
L= 8, B = 4,
∴area of floor = L × B
= 8 × 4 = 32

2 / 30

The height of a room is 5 metres and its length is twice its breadth. If 240 metres of paper of breadth 50 cm are required for papering its walls, find the area of the floor…?

1st year, A = 3x, B = 2x and C = 4x
2nd year, A = 3x, B = 2x + 270000 and C = 4x
3rd year, A = 3x, B = 2x + 270000 and
C = 4x + 270000
Total investment by A, B and C is
A = 3x + 3x + 3x = 9x
B = 2x + 2x + 2x + 270000 + 270000
= 6x + 540000
C = 4x + 4x + 4x + 270000 = 12x + 270000
After three years the ratio is 3 : 4 : 5
x = 90000.
Thus initial investment
= (3 * 90000): (2 * 90000): (4 * 90000)
` 270000, ` 180000, ` 360000

3 / 30

A, B and C enter into a partnership by investing in the ratio of 3 : 2 : 4. After one year, B invests another Rs 2,70,000 and C, at the end of 2 years invests Rs 2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find the initial investment of A, B and C…?

Let speed of the train be x km/hr and of the car be y km/hr.

Then, `120/x + 480/y = 8`

=> `1/x + 4/y = 1/5`    — (i)

And, `200/x + 400/y = 25/3`

=> `1/x + 2/y = 1/24`    — (ii)

Solving (i) and (ii), we get x = 60 and y = 80.

Ratio of speeds = 60: 80 = 3:4

4 / 30

If 120 km is done by train and the rest by car, then it takes 8 hours for a 600 km journey. Of 200 km is done by train and the rest by car, then it takes 20 minutes more. Then what would be the ratio of the speed of the train to that of the car..?

SI for 1 year will be 600 / 2 = Rs.300.
As in 1st year SI and CI are same.
So 1st year CI will also be Rs.300.
In CI, in second year 300 will also be added in principal.
So second year CI = 300 + 8% of 300 = 324.
So total CI after 2 years = 300 + 324 = Rs. 624.

5 / 30

The simple interest on a certain sum of money for 2 years at 8% p.a. is Rs. 600. What is the compound interest at the same rate and for the same time..?

Speed of boat = 15 km /hrs .
let the speed of stream be ‘s’
Given : (30/ 15+s )+ (30 /15- s) = 9/2
solving we get ,s = 5 km/hrs

6 / 30

A boat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the speed of the stream? (in km/hr)..?

T = 60/36 * 18/5 = 6 sec

7 / 30

In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way..?

Amount = Rs. (30000 + 4347) = Rs. 34347
Let the time be n years.
Then, 30000(1 +7n/100)= 34347
(107/100)^ n=34347/30000=11449/10000= (107/100)^2
n = 2 years

8 / 30

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is…?

Let x and y be the interest rates.
x% of 3 lakhs – y% of 3 lakhs = 1500
(x– y) % of 3 lakhs = 1500
300000(x – y)/100 = 1500
(x – y) = 0.5% for 2 years Þ For 1 year = 0.25%

9 / 30

The difference between the simple interest received from two different sources on Rs 3 lakhs for 2 years is rs 1,500. The difference between their rates of interest is…?

Let the original number be 10x + y
New number = 10y + x
Now, 10y + x – (10x + y) = 27
=> 9y – 9x = 27
We have, different of the two digits = 27 / 9 = 3
Sum of the two digits is = 11
Now, the two digits are (11+3 / 4) and (11-3 / 2) i.e. 7 and 4
Thus, the number is 47 because 47 < 74.
You can check it: 74 – 47 = 27

10 / 30

If the digits of a two-digit number are interchanged, the number so obtained is greater than the original number by 27. If the sum of the two digits of the number is 11, what is the original number…?

12 is an even number. All other given numbers are odd

11 / 30

Find the no which is different from other

1, 3, 9, 12, 19, 29

If the first divisor is a multiple of second divisor, then the remainder in second case = remainder obtained by dividing the first remainder by the second divisor.
Remainder = 21 ÷ 19 = 2

12 / 30

A number, when divided by 114, leaves remainder 21. If the same number is divided by 19, then the remainder will be…?

Let the speeds of bus and car be x and y. Here, y = x +25
As per the question, (500/x)-(500/x+25)=10
⇒ 500(x + 25) − 500(x) =10x(x+25) ⇒ x = 25, y = 50.
For such questions, you can also use direct substitution from the given choices

13 / 30

A car travels 25km an hour faster than a bus for a journey of 500km. If the bus takes 10 hours more than the car, then the speeds of the bus and the car are…?

Double in seven years.
So 4 times will be in = 7 × (4 − 1) = 21 years

14 / 30

A sum of money doubles itself in 7 years. In how many years it becomes four fold…?

The sum of the volumes of the new balls will equal the volume of the original ball. So, 1.5= 0.753 + 1+ r3. Solving this equation gives r = 1.25
So, d = 2.5 cm.

15 / 30

A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical balls. The diameter of two of these is 1.5 cm and 2 cm respectively. The diameter of the third ball is..?

Daily wage of woman = 15000 / (60*40) = 6.25
Therefore, daily wageof man = 2 × 6.25 = 12.5
Number of men = 6000 / (15×12.5) = 32

16 / 30

Wages for 40 women amount to Rs. 15000 in 60 days. How many men must work for 15 days to receive Rs. 6000? The daily wage of a man is double that of a woman.

Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 x 10 = 320.
Now increase in avg = 4runs. So, new avg = 32+4 = 36runs
Total runs = new avg x new no. of innings = 36 x 11 = 396
Runs made in the 11th inning = 396 – 320 = 76

17 / 30

The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4..?

Interest/Principal = 16/25
Therefore Rate = S.I * 100/Principal*Time
=> x = 16/25*100/x
⇒ x2 16 × 4 = 64
⇒ x = √64 = 8% per annum

18 / 30

Simple interest on a certain sum is 16/25 of the sum. The rate percent if the rate per cent and time (in years) are equal, is..?

Distance = 120 × 90/60 = 180 km

Speed required to cover 180 km in 1 hr 20 mins ( 4/3 hrs) =

180 × ¾ = 135 km/hr.

19 / 30

A person covers a certain distance by travelling at a uniform speed of 120 km/h for 90 minutes. At what speed will he have to travel in order to cover the same distance in 1 hour 20 minutes? (in km/h)..?

a,a+1,a+2,a+3 , let these be the numbers.
Sum=102⇒4a+6=102⇒4a=96⇒a=24
Hence extremes=24 , 27
24X27=648

20 / 30

The sum of four consecutive integers is 102. Find the product of the extremes…

Probability of drawing 1 blue pen = 4/9
Probability of drawing another blue pen = 3/8
Probability of drawing 1 black pen = 3/7
Probability of drawing 2 blue pens and 1 black pen = 4/9 * 3/8 * 3/7 = 1/14

21 / 30

 A pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, NOT replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen..?

  Let the edge = `a` cm 

So increase by `50%` = `a+a/2 = 3a/2`

Total surface Area of original cube = `6a^2`

TSA of new cube = `6(3a/2)^2`

`6 x 9a^2/4 = 13.5a^2`

Increase in area = `13.5a^2 – 6a^2 = 7.5a^2`

 `7.5a^2` Increase % = `(7.5a^2)/(6a^2) xx 100 = 125%`

22 / 30

If each edge of a cube is increased by 50%, find the percentage increase in its surface area…?

Pattern is 1 * 2, 2 * 3, 3 * 4, 4 * 5, 5 * 6, 6 * 7, 7 * 8

i.e) 8 * 9 = 72

23 / 30

Find the Missing Number 2, 6, 12, 20, 30, 42, 56, __

Let the number be equal to x.
3x/4 +75 = x
Hence x=300

24 / 30

When 75% of a number is added to 75, the result is the same number. The number is..?

Ways of selecting 3 black balls out of 5 – 5C3
Total ways of selecting 3 balls – 11C3The required probability =
5C3 / 11C3 = 10/165 = 2/33

25 / 30

A basket contains 3 blue, 5 black and 3 red balls. If 3 balls are drawn at random what is the probability that all are black..?

Clearly, l = (48 – 16)m = 32 m,

b = (36 -16)m = 20 m,

h = 8 m.

 Volume of the box = (32 x 20 x 8) m3 = 5120 m3

26 / 30

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is.

Let the CP be Rs. 100
SP = Rs 112
If the marked price be Rs. x, then 90% of x = 112
=> x = 112*100/90 = Rs. 1120/9
= 900 : 1120 = 45 : 56

27 / 30

A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is..?

We have πr2 = 7 x 2πr
∴ r = 14
∴ circumference = 2πr = 2 x (22/7) * 14 = 88

28 / 30

The magnitude of the area of a circle is seven times that of its circumference. What is the circumference (in units) of the circle..?

Let the number be x
Therefore, 0.38x – 0.24x = 135.10
We get x = 965
Thus, 0.40 × 965 = 386

29 / 30

The difference between 38% of a number and 24% of the same number is 135.10. What is 40% of that number..?

We know we can calculate it by 1/2(a+b)=> 1/2(11+5) = 1/2(16) = 8 km/hr

30 / 30

 In one hour, a boat goes 11km along the stream and 5 km against it. Find the speed of the boat in still water..?

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APTITUDE TEST 5

TOTAL QUESTIONS = 20

TOTAL TIME = 25 min

Total expenditure = 40 + 25 + 15 + 5 = 85%
Saving = (100 – 85) = 15%
15/100 × Salary = 1200, Salary = 8000 Rs

1 / 20

A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 1200, then his salary per month in rupees is…?

Interest/Principal = 16/25
Therefore Rate = S.I * 100/Principal*Time
=> x = 16/25*100/x
⇒ x2 16 × 4 = 64
⇒ x = √64 = 8% per annum

2 / 20

Simple interest on a certain sum is 16/25 of the sum. The rate percent if the rate per cent and time (in years) are equal, is..?

Let marks in English = x & Hindi = y.x/4 = y/3 Also x + y = 140. Solving the 2 equations we get x = 80

3 / 20

One-fourth of my marks in English is equal to one third of my marks in Hindi, The total number of marks secured by me in both the subjects is 140. The marks secured by me in English are…??

2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days

4 / 20

A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it…?

X = 150 + Y
X + Y = 5Y
150 + 2Y = 5Y
150 = 3Y => Y = 50.

5 / 20

A number X is 150 more than a second number, Y. If the sum of X and Y is 5 times Y, what is the value of Y..?

Since the month begins with a Sunday, to there will be five Sundays in the month.

Required average
=510 x 5 + 240 x 25
30
=8550
30
= 285

6 / 20

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is

Let x be the total income
(75/100*60/100)x + 25/100x = 42000
Solving, x = 60000

7 / 20

Suri gave 25% of her monthly salary to her mother. From the remaining salary, she paid 15% towards rent and 25%, she kept aside for her monthly expenses. The remaining amount she kept in bank account. The sum of the amount she kept in bank and that she gave to her mother was Rs. 42000. What was her monthly salary…?

Assume that P has 2x amount.
Therefore, Q = 3x amount (50% more than P)
And R = 3x × 1/3 = x
Ratio of P : Q : R = 2x : 3x : x = 2 : 3 : 1
Thus, P alone have = (2/6) × 240 = Rs. 80

8 / 20

P, Q and R have a certain amount of money with themselves. Q has 50% more than what P has, and R has 1/3rd of what Q has. If P, Q and R together have Rs. 240 then how much money does P alone have? (in Rs.)…

Let the number be x
Therefore, 0.38x – 0.24x = 135.10
We get x = 965
Thus, 0.40 × 965 = 386

9 / 20

The difference between 38% of a number and 24% of the same number is 135.10. What is 40% of that number..?

Required number = (L.C.M. of 12, 15, 20, 54) + 8 = 540 + 8 = 548

10 / 20

 The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is…?

Let the CP = 100 Rs.
Mark Price = 140
Discount = 20%
Selling price 80/100 × 140 = 112
Hence profit = 12%

11 / 20

A merchant marks his wares 40% more than the real price and allows 20% discount. His profit is…?

  Let the edge = `a` cm 

So increase by `50%` = `a+a/2 = 3a/2`

Total surface Area of original cube = `6a^2`

TSA of new cube = `6(3a/2)^2`

`6 x 9a^2/4 = 13.5a^2`

Increase in area = `13.5a^2 – 6a^2 = 7.5a^2`

 `7.5a^2` Increase % = `(7.5a^2)/(6a^2) xx 100 = 125%`

12 / 20

If each edge of a cube is increased by 50%, find the percentage increase in its surface area…?

Let the average age of the team is x years.

11x – (26+29) = 9(x-1)

x = 23

13 / 20

The captain of a cricket team of 11 players is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded the average age of remaining players is one year less than the average age whole team. What is the average age of the team…?

B received 2/3 of the profit
=> A : B = `1/3 : 2/3 = 1:2`
Let the total capital = x
Then A’s capital = `x/4`
B’s capital = `x – x/4 = (3x)/4`
Assume B’s money was used for b months
Then A:B = `(x/4)**15 : ((3x)/4)**b = 1 : 2`
=> `15/4 : (3b)/4 = 1 : 2`
=> `15 : 3b = 1 : 2`
=> `5 : b = 1 : 2`
=> `5/b = 1/ 2`
=> `b = 5**2 = 10`

14 / 20

A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B’s money was used ..?

Let marks in English = x & Hindi = y.x/4 = y/3 Also x + y = 140. Solving the 2 equations we get x = 80

15 / 20

One-fourth of my marks in English is equal to one third of my marks in Hindi, The total number of marks secured by me in both the subjects is 140. The marks secured by me in English are…??

8M = 12W s => 1M = W => ( 6M + 11W ) => D = 12W => 25 => ( 6 => W + 11W ) => D = 12W => 25 => 20 => D = 12 => 25 => D = 15 days

16 / 20

If 8 men or 12 women can do a piece of work in 25days, in how many days, can the work be done by 6 men and 11 women working together..?

3 × 5 = 15
5 × 15 = 75
15 × 75 = 112
75 × 1125 = 84375
Hence 75 is the answer.

17 / 20

What should come in place of question mark (?) : 3, 5, 15, ?, 1125, 84375..

Cost of 1 litre of water = Rs.0 = cheaper quantity.
Cost of 1 litre of juice = Rs.24 = dearer quantity.
And, the mean price = m = Rs.20
Therefore, (Cheaper quantity) : (Dearer quantity) = (d – m) : (m – c) = 4:20 = 1:5
Hence, the required answer is 1:5

18 / 20

 In what ratio,water must be mixed with fruit juice costing Rs.24 per litre so that the juice would be worth of Rs.20 per litre..?

121 = 11^2 , hence value of a = 11 and b = 2 can be considered.
Therefore, the value of (a – 1)^b + 1 = (11 – 1)^ 2 + 1= 10^3

19 / 20

 If a and b are whole numbers such that ab = 121, then find the value of (a – 1)^b + 1..?

P:Q=3:4, Q:R=5:6, P:Q:R=3×5:5×4:6×4
⇒ 15:20:24

20 / 20

If P : Q = 3 : 4 and Q : R = 5 : 6, then P : Q : R is

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