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

# Solved Examples Set 1 (Quantitative Ability)

1. 8 : ? :: 1 : 4

1. 24
2. 16
3. 0
4. 32
5. 20
? × 1 = 8 × 4
? = 32
2. If 3x = −9, then 3x3 − 2x + 4 =

1. -83
2. -71
3. -47
4. -17
5. 61
First solving 3x = −9, x = −3. Now plug into 3x3 − 2x + 4:
3x3 − 2x + 4
= 3(-3)3 − 2(-2) + 4
= 3(−27) + 6 + 4
= −81 + 6 + 4
= −71
3. 60% of 37 = ?

1. 20
2. 21
3. 22.2
4. 22
5. none
60% of 37 = 0.6 × 37 = 22.2
4. By selling a fan for $475, a person loses 5%. To get a gain of 5%, he should sell the fan for: 1.$ 500
2. $525 3.$ 535
4. $575 5.$ 505
cost price = 100/(100 - 5) x 475 = $500 sale price = (100 + 5)/100 x 500 =$ 525
5. A girl is 18 years younger than her mother. In 6 years time, the sum of their ages will be 54.How old is the girl now?

1. 10 years
2. 11 years
3. 12 years
4. 13 years
5. 14 years
Let girl's age = x
then mother's age = x + 18
After 6 years,
x + 6 + x + 18 + 6 = 54
2x + 30 = 54
2x = 24
x = 12
6. 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
7. 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 = $451000 8. A man sells two houses for$ 2 lac each. On one he gained 20% and on the other he lost 20%. His total profit or loss % in the transaction will be

1. 4% profit
2. 5% loss
3. no profit, no loss
4. 4% loss
5. 3% loss
% loss = (% loss X % profit)/100 = (20 X 20)/100 = 4%
9. $${2244 \over 0.88} = ? × 1122$$

1. 20.02
2. 20.2
3. 19.3
4. 2.27
5. 3.27
$${2244 \over 0.88} = ? × 1122$$
$$? = {2550 \over 1122} = 2.27$$
10. A shopkeeper sold two articles for $48 each. He made a 25% profit on one article and a loss of 20% on the other. What was his net gain or loss on the sale of the two articles? 1. loss of$ 1.40
2. gain of $2.40 3. loss of$ 2.40
4. gain of $1.40 5. gain of$ 2.60
25% profit at selling price $48 = 48 x .25 =$ 12
20% loss at selling price $48 = 48 x 0.2 =$ 9.6
gain = profit - loss = 12 - 9.6 = $2.4 11. ?% of 60 = 24 1. 40 2. 48 3. 45 4. 42 5. 38 ?% × 60 = 24 $$? = {24 \over 60} × 100$$ = 40 12. A man earned an annual income of$ 245000 in 1990. He was allowed a deduction of $15000 relief for each of his three children and a personal relief of$ 30000. If he was charged a tax rate of 4% on first $50000 and 6% on his remaining income, calculate the total tax charged. 1.$ 9200
2. $8700 3.$ 9500
4. $9400 5.$ 9000
Total Income = $245000 Total relief = 3 × 15000 + 30000 =$ 75000
Rest income = 245000 - 75000 = 170000
Tax on 1st 50000 = 0.04 × 50000 = $2000 Tax on rest amount 120000 = 0.06 × 120000 =$ 7200
Total tax = 200 + 7200 = $9200 13. 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. 14. 5.41 - 3.29 × 1.6 = ? 1. 14.6 2. 0.3392 3. 0.146 4. 3.392 5. 1.46 5.41 - 3.29 × 1.6 = 5.41 - 5.264 = 0.146 15. ? × 12 = 75% of 336 1. 48 2. 252 3. 28 4. 21 5. 23 ? × 12 = 75% of 336 ? × 12 = 0.75 × 336 ? × 12 = 252 $$? = \frac{252}{12}$$ ? = 21 16. 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 17. Rashid buys three books for$ 16 each and four books for $23 each, what will be the average price of books 1.$ 18
2. $20 3.$ 22
4. $24 5.$ 16
Price of 3 books = 3 × 16 = $48 Price of 4 books = 4 × 23 =$ 92
Total price = $140 Total books = 3 + 4 = 7 Average price of books = $$140 \over 7$$ =$ 20
18. A certain solution is to be prepared by combining chemicals X, Y and Z in the ratio 18:3:2. How many liters of the solution can be prepared by using 36 liters of X?

1. 46 liters
2. 47 liters
3. 45 liters
4. 49 liters
5. 44 liters
As total ratio is 18 +3 + 2 = 23
Let total solution is x liters
Then $$18 \over 23$$ x = 36
x = $$36 × 23 \over 18$$ = 46 liters
19. 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
20. The amount of hot cocoa powder remaining in a can is 6 1⁄4 tablespoons. A single serving consists of 1 3⁄4 tablespoons of the powder. What is the total number of servings of the powder remaining in the can?

1. 3 1⁄2
2. 3 4⁄7
3. 4 3⁄7
4. 4 1⁄2
5. 6
As $$6\frac{1}{4} = \frac{25}{4}$$ and $$1\frac{3}{4} = \frac{7}{4}$$. Therefore,
$$\frac{6\frac{1}{4} \text{ tsp}}{1\frac{3}{4} \text{ } \frac{tsp}{ serving}} = \frac{\frac{25}{4}}{\frac{7}{4}} \text{ servings} = \frac{25}{7} \text{ servings} = 3\frac{4}{7} \text{ servings}$$