Aptitude Training

01

What is 15% of 240?

240 ?? 15/100 = 36.

02

A number increased by 25% becomes 500. Find the number.

Number = 500 / 1.25 = 400.

03

What percentage of 80 is 20?

(20/80) ?? 100 = 25%.

04

If a shirt costs 800 and the discount is 20%, what is the selling price?

SP = 800 ?? 0.80 = 640.

05

A shopkeeper buys at 100 and sells at 125. Find the profit percentage.

Profit = 25, profit% = 25%.

06

An article is sold at a 10% loss. If the selling price is 450, find the cost price.

CP = 450 / 0.90 = 500.

07

Successive discounts of 10% and 20% equal a single discount of how much?

1 ??? (0.9 ?? 0.8) = 1 ??? 0.72 = 28%.

08

If the price of an item is increased by 20% and then decreased by 20%, net change is?

Net = ???4% (decrease). 1.2 ?? 0.8 = 0.96.

09

A student scores 45 out of 60 in a test. What is the percentage?

(45/60) ?? 100 = 75%.

10

Find the average of 12, 15, 18, 21, 24.

Sum = 90, average = 90/5 = 18.

11

The average of 10 numbers is 20. If one number is removed, the average of the rest is 18. Find the removed number.

Sum of 10 = 200, sum of 9 = 162, removed = 38.

12

The average age of 5 people is 25. What is their total age?

Total = 5 ?? 25 = 125.

13

A batsman scores 40, 60, 50, 30, 70 in five innings. Find the average.

Sum = 250, average = 50.

14

If the average of three numbers is 12 and two are 10 and 14, find the third.

Total = 36, third = 36 ??? 24 = 12.

15

Find the ratio of 250 g to 2 kg.

250 : 2000 = 1 : 8.

16

If a : b = 2 : 3 and b : c = 4 : 5, find a : b : c.

a : b : c = 8 : 12 : 15.

17

Divide 90 in the ratio 2 : 3.

Parts are 36 and 54.

18

The ratio of ages of two persons is 4 : 5 and their sum is 45. Find their ages.

Ages are 20 and 25.

19

If 5 men can build a wall in 10 days, how long will 10 men take?

Time = (5 ?? 10)/10 = 5 days.

20

A and B together can finish a work in 6 days; A alone in 10 days. In how many days can B alone do it?

B alone = 1/(1/6 ??? 1/10) = 15 days.

21

12 workers do a job in 8 days. How many workers are needed to finish in 6 days?

Workers = (12 ?? 8)/6 = 16.

22

A pipe fills a tank in 12 hours and another empties it in 18 hours. Time to fill?

Net rate = 1/12 ??? 1/18 = 1/36, so 36 hours.

23

A train covers 180 km in 3 hours. Find its speed in km/h.

Speed = 180/3 = 60 km/h.

24

A train 200 m long crosses a pole in 10 seconds. Find its speed in km/h.

Speed = 200/10 = 20 m/s = 72 km/h.

25

Convert 54 km/h into m/s.

54 ?? 5/18 = 15 m/s.

26

A car travels 240 km at 40 km/h. Find the time taken.

Time = 240/40 = 6 hours.

27

Two trains 100 m and 120 m long run at 40 and 50 km/h in opposite directions. Time to cross?

Relative speed = 90 km/h = 25 m/s. Time = 220/25 = 8.8 s.

28

A boat travels 20 km downstream in 2 hours and upstream in 5 hours. Find the boat speed.

Down = 10, up = 4. Boat = (10+4)/2 = 7 km/h.

29

The speed of a stream is 2 km/h and a boat goes 12 km downstream in 1.5 h. Find the boat speed in still water.

Down = 8. Boat = 8 ??? 2 = 6 km/h.

30

A man covers half the distance at 20 km/h and half at 30 km/h. Average speed?

Avg = 2??20??30/(20+30) = 24 km/h.

31

The sum of two numbers is 60 and their difference is 20. Find the numbers.

Numbers are 40 and 20.

32

Three consecutive integers add to 36. Find the middle one.

Middle = 36/3 = 12.

33

Find the largest of the numbers that divides 2, 4, 6, 8 exactly.

HCF of 2,4,6,8 = 2.

34

Find the HCF of 12 and 18.

HCF = 6.

35

Find the LCM of 6 and 8.

LCM = 24.

36

The LCM and HCF of two numbers are 60 and 6. If one is 12, find the other.

Other = (60 ?? 6)/12 = 30.

37

Find the smallest number divisible by 2, 3, 4, 5.

LCM of 2,3,4,5 = 60.

38

A number when divided by 7 leaves remainder 3. What is the remainder when double the number is divided by 7?

2 ?? 3 = 6.

39

Find the number of factors of 36.

36 = 2????3??, factors = 3??3 = 9.

40

Is 89 a prime number?

Yes, it has no factors other than 1 and 89.

41

The product of two numbers is 240 and their HCF is 4. Find their LCM.

LCM = 240/4 = 60.

42

Find the square of 25.

625.

43

Find the cube root of 216.

6.

44

Simplify: 25 ??? 4 ?? 5 + 6.

25 ??? 20 + 6 = 11.

45

What is the value of 2^5?

32.

46

Find 0.25 as a fraction in lowest terms.

1/4.

47

Express 3/5 as a decimal.

0.6.

48

What is the simple interest on 5000 at 8% per annum for 2 years?

SI = 5000 ?? 0.08 ?? 2 = 800.

49

Find the compound interest on 10000 at 10% for 2 years.

Amount = 12100, CI = 2100.

50

At what rate percent will 4000 earn 800 simple interest in 2 years?

Rate = 800/(4000??2) = 10%.

51

The difference between CI and SI on 1000 at 10% for 2 years is?

Diff = 10.

52

A sum doubles itself in 8 years at simple interest. Find the rate.

Rate = 100/8 = 12.5%.

53

In how many years will 6000 amount to 9000 at 10% simple interest?

Time = 3000/(6000??0.1) = 5 years.

54

A shopkeeper mixes 10 kg of tea at 300 per kg with 10 kg at 500 per kg. Cost of the mixture?

(300??10 + 500??10)/20 = 400 per kg.

55

In what ratio must rice at 40 per kg be mixed with rice at 60 per kg to sell at 50?

Equal ratio, 1 : 1.

56

A man invests 4000 at 5% and 6000 at 8%. Overall rate?

(200 + 480)/10000 = 6.8%.

57

Find the value of x if 3x + 7 = 22.

x = 5.

58

Solve: 2(x ??? 3) = 8.

x ??? 3 = 4, so x = 7.

59

The sum of an angle and its complement is 90??. If the angle is 30??, find its complement.

Complement = 60??.

60

The angles of a triangle are in the ratio 2 : 3 : 4. Find the largest angle.

Sum = 9 parts = 180??, largest = 80??.

61

Find the area of a square whose side is 12 cm.

Area = 144 cm??.

62

Find the perimeter of a rectangle 8 m by 5 m.

Perimeter = 2(8+5) = 26 m.

63

Find the area of a rectangle 8 m by 5 m.

Area = 40 m??.

64

Find the circumference of a circle of radius 7 cm (?? = 22/7).

2??r = 44 cm.

65

Find the area of a circle of radius 7 cm (?? = 22/7).

??r?? = 154 cm??.

66

Find the volume of a cube of side 3 cm.

27 cm??.

67

The length of a diagonal of a square of side 10 is?

10???2 cm.

68

In how many ways can 4 people stand in a line?

4! = 24 ways.

69

In how many ways can 3 books be arranged on a shelf?

3! = 6 ways.

70

How many ways to select 2 students from 5?

C(5,2) = 10.

71

How many 2-digit numbers can be formed from digits 1, 2, 3 without repetition?

3 ?? 2 = 6.

72

The number of ways to arrange the letters of CAT?

3! = 6.

73

What is the probability of getting heads on a single coin toss?

1/2.

74

A die is rolled once. Probability of an even number?

3/6 = 1/2.

75

A bag has 3 red and 5 green balls. Probability of picking a green?

5/8.

76

Two dice are rolled. Probability that the sum is 7?

6/36 = 1/6.

77

Probability of drawing an ace from 52 cards?

4/52 = 1/13.

78

What is the next number: 3, 6, 9, 12, 15, ?

18.

79

Find the next term: 1, 4, 9, 16, 25, ?

36 (squares).

80

Find the next term: 2, 4, 8, 16, 32, ?

64.

81

Find the odd one out: 3, 5, 7, 8, 11.

8 (only even / non-prime).

82

Find the next term: 1, 1, 2, 3, 5, 8, ?

13 (Fibonacci).

83

If 6 is coded as G and 20 as T, how is 12 coded?

L (12th letter).

84

If CAT is coded as DBU, how is DOG coded?

EPH (each letter +1).

85

If A = 1, B = 2, what is the code for BAD?

BAD = 2, 1, 4.

86

Rohan walks 5 km north then 5 km south. How far is he from the start?

0 km (he returns).

87

A person walks 4 km east, then 3 km north. Shortest distance from start?

5 km (3-4-5 triangle).

88

If east is coded as west in a code, which direction is 180?? from north?

South.

89

Pointing to a man, a woman says he is the son of my mother. How is the man related to her?

Brother.

90

A is the father of B and B is the sister of C. How is A related to C?

Father.

91

If today is Monday, what day is after 3 days?

Thursday.

92

If 15th of a month is Wednesday, what day is the 1st of the month?

Wednesday minus 14 = Wednesday.

93

How many Sundays are there in a normal year of 365 days?

At least 52.

94

At what time between 3 and 4 do the hands of a clock overlap?

3:16:21 approximately.

95

The angle between the clock hands at 3:00?

90??.

96

A number increased by 30% and then decreased by 30% gives?

Net = ???9%.

97

If 6 men can do a work in 15 days, how many men are needed to do it in 9 days?

Men = (6 ?? 15)/9 = 10.

98

Find 20% of 20% of 500.

0.2 ?? 0.2 ?? 500 = 20.

99

A sells an item for 264 at a 12% profit. Find the cost price.

CP = 264/1.12 = 235.71.

100

In how many days will 12 men and 8 women do a work if 1 man = 2 women?

Treat 8 women as 4 men, so 16 men. If 12 men take... use constant product: 12 men in d days, here 16 men: d = (12??d0)/16.