In the name of ALLAH, the most beneficient, the most merciful

# Solved Examples Set 1 (Quantitative Ability)

1. 40 men can build a wall 4 metres high in 15 days. The number of men required to build a similar wall 5 metres high in 6 days is

1. 115
2. 125
3. 105
4. 135
5. 130
$$40 × 15 × 5 \over 6 × 4$$ = 125 men
2. A man bought a flat for $820000. He borrowed 55% of this money from a bank. How much money did he borrow from the bank? 1.$ 451000
2. $452000 3.$ 453000
4. $454000 5.$ 450000
55% of 820000 = 0.55 × 820000 = $451000 3. 60% of 37 = ? 1. 20 2. 21 3. 22.2 4. 22 5. none 60% of 37 = 0.6 × 37 = 22.2 4. 5789 - 2936 + 1089 = ? 1. 3942 2. 4041 3. 2626 4. 3932 5. 3940 5789 - 2936 + 1089 = 6878 - 2936 = 3942 5. 12% of ________ = 48 1. 250 2. 100 3. 400 4. 200 5. 300 $$12 \text{% of } x = 48$$ $$0.12x = 48$$ $$x = \frac{48}{0.12} = 400$$ 6. 8 : ? :: 1 : 4 1. 24 2. 16 3. 0 4. 32 5. 20 ? × 1 = 8 × 4 ? = 32 7. If 4a + 2 = 10, then 8a + 4 = 1. 5 2. 16 3. 20 4. 24 5. 28 One may answer this question by solving 4a + 2 = 10 4a = 8 a= 2 Now, plugging in 2 for a: 8a + 4 = 8(2) + 4 = 20 A faster way of solving this is to see the relationship between the quantity 4a + 2 (which equals 10) and 8a + 4. Since 8a + 4 is twice 4a + 2, the answer must be twice 10, or 20. 8. A group of laborers accepted to do a piece of work in 20 days. 8 of them did not turn up for the work and the remaining did the work in 24 days. The original number of laborers was 1. 47 2. 48 3. 49 4. 50 5. 51 x laborers do work in 20 days and x-8 laborers do same work in 24 days. As the no. of laborers decrease, the no. of days increased then it becomes as x : x - 8 :: 24 : 20 product of interiors = product of exteriors 24x - 192 = 20x 4x = 192 x = 48 9. A man takes 50 minutes to cover a certain distance at a speed of 6 km/hr. If he walks with a speed of 10 km/hr, he covers the same distance in 1. 1 hour 2. 30 minutes 3. 20 minutes 4. 10 minutes 5. 40 minutes $$50 × 6 \over 10$$ = 30 minutes 10. A shopkeeper bought a radio from a wholesaler for$ 250.00. In addition, he paid a sales tax of 15% on the cost price. He then sold the radio for $315.00. Calculate the cash profit made by the shopkeeper. 1.$ 20.00
2. $22.50 3.$ 25.00
4. $27.50 5.$ 27.00
cost price = $250 sales tax = .15 × 250 =$ 37.5
cash profit = 315 - 250 - 37.5 = $27.5 11. Rashid's salary was reduced by 20%. In order to restore his salary at the original amount, it must be raised by 1. 20% 2. 22.50% 3. 25% 4. 26% 5. 27% Let Rashid's Salary 100 20% reduced salary is 80 As the reduced amount is 20 So what percentage of the present sallary is required to be equal to 20? ?% of 80 = 20 ? = $$20 \over 80$$ × 100 = 25% 12. if x% of 60 = 48 then x = ? 1. 80 2. 60 3. 90 4. 40 5. 70 x = $${48 × 100 \over 60}$$ = 80 13. At a book fair, a book was reduced in price from$ 75 to $60. If the first price gives a 50% profit, find the percentage profit of the book sold at the reduced price. 1. 20% 2. 30% 3. 40% 4. 50% 5. 10% As$ 75 (first price) gives a profit = 50%
$1 gives a profit = (50/75)%$ 60 (reduced price) gives profit = (50/75 x 60)% = 40%
14. A man is 5 times as old as his son. 2 years ago the sum of the squares of their ages was 1114. Find the present age of son.

1. 7 years
2. 9 years
3. 8 years
4. 8 1/2 years
5. 6 years
Let son's age = x, then
father's age = 5x
As before 2 years ago the sum of the squares of their ages was 1114, the equation becomes as
$$(x - 2)^2 + (5x - 2)^2 = 1114$$
By simplifying the equation, we have
$$13x^2 -12x -553 = 0$$
Now solving the equation, we have
$$13x^2 - 12x - 553 = 0$$
$$13x^2 - 91x + 79x -553 = 0$$
13x(x - 7) + 79(x - 7) = 0
(x - 7)(13x + 79) = 0
x = 7 and x = -6.077
As age could not be negative, hence the present age of the son is 7 years.
15. 1.02 - 0.20 + ? = 0.842

1. 0.222
2. 232
3. 2
4. 0.022
5. 0.012
1.02 - 0.20 + ? = 0.842
0.82 + ? = 0.842
? = 0.842 - 0.82 = 0.022
16. In the series 8, 9, 12, 17, 24 . . . the next number would be

1. 29
2. 30
3. 33
4. 35
5. 41
In the series, 8, 9, 12, 17, 24 . . .
9 − 8 = 1
12 − 9 = 3
17 − 12 = 5
24 − 17 = 7
Hence, the difference between the next term and 24 must be 9 or
x − 24 = 9, and
x = 33
Hence, the next term in the series must be 33
17. A bank increased the rate of interest which it paid to depositors from 3.5% to 4% per annum. Find how much more interest a man would receive if he deposited $64000 in the bank for 6 months at the new interest rate 1.$ 160
2. $180 3.$ 200
4. $220 5.$ 150
If the interest rate is 3.5% then interest amount is
3.5% of 6400 = 0.035 × 6400 = $2240 If the interest rate is 4% then interest amount is 4% of 6400 = 0.04 × 6400 =$ 2560
Now the difference of both interests = 2560 - 2240 = $320 per annum Interest for half year (6 months) = $$320 \over 2$$ =$ 160
18. $${396 \over 11}$$ + 19 = ?

1. 19.8
2. 36
3. 55
4. 33
5. 50
$${396 \over 11}$$ + 19 = 36 + 19 = 55
19. A man walked for 3 hours at 4.5 km/h and cycled for some time at 15 km/h. Altogether, he traveled 21 km. Find the time taken for cycling.

1. 1/2 hour
2. 1 hour
3. 1 1⁄2 hours
4. 2 hours
5. 2 1⁄2 hours
The man walked the distance = 3 x 4.5 = 13.5 km. The distance cycled by the man = 21 - 13.5 = 7.5 km
As he cyled 15 km in 1 h
he cycled 1 km in 1/15 h
Finally, he cycled 7.5 km in 7.5/15 = 1/2 h
20. A boy of height 165 cm is replaced by another, which decreases the average height of the group of 34 students, by 1 cm. The height of the new student is

1. 129 cm
2. 130 cm
3. 131 cm
4. 132 cm
5. 133 cm
Total decreased height of 34 students = 1 × 34 = 34 cm
Height of the replaced student = 165 - 34 = 131 cm