Quantitative Aptitude Trivia Quiz!

1. By selling an item at a certain price, a merchant gains 20%. If he sells it at the double price, then the profit percentage will be?

40

100

120

140

Assuming CP as x and then you can procced solving. But its time consuming.

Just assume CP = 100. Profit 20%, So, SP = 120
Now its sold at double the price. So new SP will be 120*2 = 240.
Now profit percentage will be 140%.

Explanation

Assuming CP as x and then you can procced solving. But its time consuming.

Just assume CP = 100. Profit 20%, So, SP = 120
Now its sold at double the price. So new SP will be 120*2 = 240.
Now profit percentage will be 140%.

2. How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?

36

42

54

63

Apply the rule of Alligation.
9 per kg should be mixed with 7 per kg to get the mixture costing 8.4 per kg (Not 9.24 as it is SP)
Note : SP = 9.24, profit = 10%. So CP = 8.4

So the ratio will be 7:3.
3 parts corresponds to 72 kg. So 7 parts will be 63 Kg.

Explanation

Apply the rule of Alligation.
9 per kg should be mixed with 7 per kg to get the mixture costing 8.4 per kg (Not 9.24 as it is SP)
Note : SP = 9.24, profit = 10%. So CP = 8.4

So the ratio will be 7:3.
3 parts corresponds to 72 kg. So 7 parts will be 63 Kg.

3. Compare x and y6 x² – 19 x + 15 = 010 y² – 29 y + 21 = 0

X>y

X

X ≥ y

X ≤ y

X = y or no relation can be established between ‘x’ and ‘y’

Solving we get, x = 10/6, 9/6 and y = 14/10, 15/10

10/6 > 14/10
10/6 > 15/10
9/6 > 14/10
9/6 = 15/10

Explanation

Solving we get, x = 10/6, 9/6 and y = 14/10, 15/10

10/6 > 14/10
10/6 > 15/10
9/6 > 14/10
9/6 = 15/10

4. Painter A can paint a house in 16 days, and painter B can do the same work in 20 days. With the help of painter C, they paint the house in 8 days only. Then, Painter C alone can do this task in ___ days.

80

85

79

76

Avoid fractions in time and work. Apply LCM method.
Basic rule to remember is Efficiency * Time taken = Total work
Assume total work = LCM (16, 20, 8) = 80.
Efficiency of A is 80/16 = 5 work/day.
Efficiency of B is 80/20 = 4 work/day.
Efficiency of (A+B+C) = 80/8 = 10 work/day.
So efficiency of C will be 10 - (4+5) = 1 work/day.
Hence time taken by C will be 80/1 = 80 days

Explanation

Avoid fractions in time and work. Apply LCM method.
Basic rule to remember is Efficiency * Time taken = Total work
Assume total work = LCM (16, 20, 8) = 80.
Efficiency of A is 80/16 = 5 work/day.
Efficiency of B is 80/20 = 4 work/day.
Efficiency of (A+B+C) = 80/8 = 10 work/day.
So efficiency of C will be 10 - (4+5) = 1 work/day.
Hence time taken by C will be 80/1 = 80 days

5. If the price of an item is decreased by 10% and then increased by 10%, the net effect on the price of the item is:

1% decrease

10% increase

1% increase

10% decrease

No change

Concept of successive percentage change
X = (a+b) + (a*b)/100
a, b are the changes. x is the resultant.
a = +10
b = -10
Solving we get, x value -1
So Net effect is 1% decrease.

We can also assume initial value to be 100. Now decreasing 10% we get 90. Now again increasing 10% on 90 we get 99.
So Net effect is drop from 100 to 99. i.e 1 % decrease

Explanation

Concept of successive percentage change
X = (a+b) + (a*b)/100
a, b are the changes. x is the resultant.
a = +10
b = -10
Solving we get, x value -1
So Net effect is 1% decrease.

We can also assume initial value to be 100. Now decreasing 10% we get 90. Now again increasing 10% on 90 we get 99.
So Net effect is drop from 100 to 99. i.e 1 % decrease

6. A paddleboat can row at 13 km/hr in still water. Find the time taken (in hours) by the paddleboat to travel 68 km along the stream, if the speed of the stream is 4 km/hr.

2

3

4

5

Speed of boat -x
Speed of water - y
Upstream speed = x-y
Downstream speed = x+y

We know Distance = Speed * Time

So time = 68 / (13+4) = 4 hours

Explanation

Speed of boat -x
Speed of water - y
Upstream speed = x-y
Downstream speed = x+y

We know Distance = Speed * Time

So time = 68 / (13+4) = 4 hours

7. ___, 11, 24, 75, 304

8

5

10

9

The pattern is Multiply by 1 and add 1, multiply by 2 and add 2, etc..

10*1+1 = 11
11*2+2 = 24,
..........
........

Explanation

The pattern is Multiply by 1 and add 1, multiply by 2 and add 2, etc..

10*1+1 = 11
11*2+2 = 24,
..........
........

8. The surface area of a cuboid is 88 sq.cm, and its edges are in the ratio 1 : 2 : 3. What is the volume the cuboid (in cubic metre) ?

24

64

48

44

Surface Area = 2*(lb + bh + hl)
l-length, b-breadth, h-height

1:2:3 will be the 3 dimensions. So 1x, 2x, 3x

Thus 88 = 2* (1x*2x + 2x*3x + 3x*1x) = 2 * 11 x^2
x= 2
So volume equals l * b * h, i.e 2*4*6 = 48 cubic metre

Explanation

Surface Area = 2*(lb + bh + hl)
l-length, b-breadth, h-height

1:2:3 will be the 3 dimensions. So 1x, 2x, 3x

Thus 88 = 2* (1x*2x + 2x*3x + 3x*1x) = 2 * 11 x^2
x= 2
So volume equals l * b * h, i.e 2*4*6 = 48 cubic metre

9. How many words can be formed by using all the letters of the word 'DAUGHTER' so that the vowels always come together?

4320

4325

4200

4326

Given word contains 8 different letters.
When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter.
Then, the letters to be arranged are DGHTR(AUE). These 6 letters can be arranged in 6P6 = 6! = 720 ways.
The vowels in the group (AUE) may be arranged in 3! = 6 ways.
Required number of words = (720 x 6) = 4320.

Explanation

Given word contains 8 different letters.
When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter.
Then, the letters to be arranged are DGHTR(AUE). These 6 letters can be arranged in 6P6 = 6! = 720 ways.
The vowels in the group (AUE) may be arranged in 3! = 6 ways.
Required number of words = (720 x 6) = 4320.

10. The average monthly salary of 20 employees in a factory is Rs. 1500. If the salary of manager is added, then the average salary increases by Rs. 100. Find the monthly salary of manager?

3100

2600

3600

2880

Average = Total salary of employees / No. of employees.
Salary of the manager = Rs. (1600x21 - 1500x20) = Rs. 3600

Explanation

Average = Total salary of employees / No. of employees.
Salary of the manager = Rs. (1600x21 - 1500x20) = Rs. 3600

11. Two cyclist begin training on an oval racecourse at the same time. The professional cyclist completes each lap in 4 minutes; the novice takes 6 minutes to complete each lap. How many minutes after the start will both cyclist pass at exactly the same spot where they began to cycle?

8

10

12

14

This question is an application of LCM.
LCM of 4, 6 = 12

Explanation

This question is an application of LCM.
LCM of 4, 6 = 12

12. In how many ways can 3 distinct letters can be posted in 5 distinct postboxes?

27

15

125

60

Consider letter point of view. 1st letter can be posted in any of the five postboxes. Similarly letter 2 and letter 3. Each 5 ways. So the total number of ways will be 5 * 5 * 5 = 125

For these kind of problems, remember this . (Immovable)^ Movable
Postboxes - Immovable and Letters - movable

Explanation

Consider letter point of view. 1st letter can be posted in any of the five postboxes. Similarly letter 2 and letter 3. Each 5 ways. So the total number of ways will be 5 * 5 * 5 = 125

For these kind of problems, remember this . (Immovable)^ Movable
Postboxes - Immovable and Letters - movable

13. When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 11?

1/12

11/12

3/11

11/36

This is a pattern. Try to remember this.

P (Sum less than or equal to 11) = Total probability - (Sum greater than or equal to 11)

= 1 - (2+1)/36 = 1-1/12 = 11/12

Explanation

This is a pattern. Try to remember this.

P (Sum less than or equal to 11) = Total probability - (Sum greater than or equal to 11)

= 1 - (2+1)/36 = 1-1/12 = 11/12

14. Present ages of Ram and Shyam are in the ratio of 4 : 5 respectively. Five years hence the ratio of their ages becomes 5 : 6 respectively. What is Ram's present age?

25

22

20

30

Ram - R and Shyam - S.
(R+5) / (S+5) = 5/6
Present age ratio is 4:5, so R = 4x and S = 5x
Solving we get, R=20

Explanation

Ram - R and Shyam - S.
(R+5) / (S+5) = 5/6
Present age ratio is 4:5, so R = 4x and S = 5x
Solving we get, R=20

15. A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:

25

20

16.66

12.5

This can be solved using alligation concept. For this question, rule of alligation is lengthy.

Alternate approach:

Think logically. Gain % = 25, i.e 1/4 gain.
Here gain is because of addition of water. So considering 4 parts to be milk, 1 part extra water is added.
So total we have 5 parts. Water 1 part and milk 4 parts.
Thus, percentage of water in the mixture is 1/5 = 20%

Explanation

This can be solved using alligation concept. For this question, rule of alligation is lengthy.

Alternate approach:

Think logically. Gain % = 25, i.e 1/4 gain.
Here gain is because of addition of water. So considering 4 parts to be milk, 1 part extra water is added.
So total we have 5 parts. Water 1 part and milk 4 parts.
Thus, percentage of water in the mixture is 1/5 = 20%

16. 115% of 4880 - 85% of 1640 = ?

4018

3978

4218

4320

115% = 100% + 10% + 5%
100% of 4880 = 4880
10% of 4880 = 488
5% of 4880 = 244.

85% = 100% - 10% - 5%
100% of 1640 = 1640
10% of 1640 = 164
5% of 1640 = 82

Solving we get,

Explanation

115% = 100% + 10% + 5%
100% of 4880 = 4880
10% of 4880 = 488
5% of 4880 = 244.

85% = 100% - 10% - 5%
100% of 1640 = 1640
10% of 1640 = 164
5% of 1640 = 82

Solving we get,

17. What is the total number of divisors of 600 (including 1 and 600)?

23

24

25

26

Prime factorizing 600 we get 2^3 * 3^1 * 5^2
So no of factors will be 4*2*3 = 24
1 and 600 are also factors and they are included in the calculation.

Explanation

Prime factorizing 600 we get 2^3 * 3^1 * 5^2
So no of factors will be 4*2*3 = 24
1 and 600 are also factors and they are included in the calculation.

18. Read the graph and answer questions . Income and Expenditure of a company over the year (in lakhs of rupees).

The ratio of the average income of all the years to the average profit is:

24:13

48:17

12:7

6:5

Profit = Income = Expenditure
Total income = (30 + 50 + 40 + 60 + 60) = 240
Total profit = (10 + 20 + 10 + 20 + 25) = 85
So Ratio = (240/5) / (85/5) = 48/17

Explanation

Profit = Income = Expenditure
Total income = (30 + 50 + 40 + 60 + 60) = 240
Total profit = (10 + 20 + 10 + 20 + 25) = 85
So Ratio = (240/5) / (85/5) = 48/17

19. A box contains 10 red and 10 yellow balls. The probability of drawing two balls of the same color is:

10/19

5/19

9/19

9/38

Total number of balls = 20.
Let S be the sample space. Then,
n(S) = Number of ways of drawing 2 balls out of 20 = 20C2
Let E = event of drawing 2 balls of the same color.
n(E) = 10c2 + 10c2 (Both red or both yellow)
So P(E) = n(E) / s(E)
Solving we get 9/19

Explanation

Total number of balls = 20.
Let S be the sample space. Then,
n(S) = Number of ways of drawing 2 balls out of 20 = 20C2
Let E = event of drawing 2 balls of the same color.
n(E) = 10c2 + 10c2 (Both red or both yellow)
So P(E) = n(E) / s(E)
Solving we get 9/19

20. Read the graph and answer questions . Income and Expenditure of a company over the year (in lakhs of rupees).

What is the percentage increase of profit from 1982 to 1983?

20%

100%

50%

200%

Profit in 1982 = 10
Profit in 1983 = 20
Percentage increase = (20-10)/10 * 100 = 100%

Explanation

Profit in 1982 = 10
Profit in 1983 = 20
Percentage increase = (20-10)/10 * 100 = 100%