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

# Solved Examples Set 1 (Quantitative Ability)

1. After spending 88% of his income, a man had $2160 left. Find his income. 1.$ 18000
2. $19000 3.$ 20000
4. $22000 5.$ 17000
Let income = x
x = 88% of x + 2160
x - 0.88x = 2160
0.12x = 2160
x = $$216000 \over 12$$ = 18000
2. 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% 3. 12% of ________ = 48 1. 250 2. 100 3. 400 4. 200 5. 300 $$12 \text{% of } x = 48$$ $$0.12x = 48$$ $$x = \frac{48}{0.12} = 400$$ 4. 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 5. 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% 6. if a > b and b > c then: 1. a = c 2. a > c 3. c > a 4. a < c 5. none As a > b > c so a > c 7. A bank exchanges British currency for Singapore currency at the rate of S$ 3.20 to pond 1. Calculate, in Pond, the amount exchanged for S$1,600 by a customer who also had to pay an extra 3% commission for this transaction. 1. Pond 475 2. Pond 485 3. Pond 495 4. Pond 505 5. Pond 510 As commission is 3% of 1600 = 0.03 × 1600 = S$ 48
the rest amount = 1600 - 48 = S$1552 S$ 1 = $$1 \over 3.20$$ = Pond 0.3125
Now S$1552 = 1552 × 0.3125 = Pond 485 8. A man pays 10% of his income for his income tax. If his income tax amounts to$ 1500, what is his income?

1. $13000 2.$ 15000
3. $17000 4.$ 19000
5. $11000 Let x = income 10% of x =$ 1500
0.1x = $1500 x = $$1500 \over 0.1$$ =$ 15000
9. $$25 \text{% of }{4 \over 4\text{%}} \text{ of }{1 \over 25} = ?$$

1. 1
2. 3
3. 0
4. 67
5. 25
$$25 \text{% of }{4 \over 4\text{%}} \text{ of }{1 \over 25}$$
$$= 25 \text{% } × {4 \over 4\text{%}} × {1 \over 25}$$
$$= 0.25 × {4 \over 0.04} × {1 \over 25}$$
$$= {25 \over 25}$$
= 1
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. $${5.76 \over 1.6} - 2.4 = ?$$ 1. 1.2 2. 2.4 3. 7.2 4. 0.12 5. 0.012 $${5.76 \over 1.6} - 2.4 =$$ 3.6 - 2.4 =1.2 12. On a trip to visit friends, a family drives 65 miles per hour for 208 miles of the trip. If the entire trip was 348 miles and took 6 hours, what was the average speed, in miles per hour, for the rest of the trip? 1. 44 2. 50 3. 51 4. 58 5. 60 As the first part of the trip took $$\frac{208 \text{ miles}}{65 \text{ } \frac{miles}{hour}} = 3.2 \text{ hours},$$ so the remaining 140 miles (348 - 208) took 2.8 hours (6 - 3.2). The average speed for the rest of the trip was $$\frac {140 \text{ miles}}{2.8 \text{ hours}} = 50$$ miles per hour. 13. 350 × ? = 4200 1. 12 2. 24 3. 15 4. 30 5. 16 $$? = {4200 \over 350} =12$$ 14. 5873 + 12034 + 1106 = ? 1. 19016 2. 20001 3. 19013 4. 2018 5. 19010 5873 + 12034 + 1106 = 17907 + 1106 = 19013 15. $${2244 \over 0.88} = ? × 1122$$ 1. 20.02 2. 20.2 3. 19.3 4. 2.27 5. 3.27 $${2244 \over 0.88} = ? × 1122$$ $$? = {2550 \over 1122} = 2.27$$ 16. 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
17. ? × 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

18. In the figure above, AB is one edge of a cube. If AB equals 5, what is the surface area of the cube?

1. 25
2. 100
3. 125
4. 150
5. 300
Since one edge of the cube is 5, all edges equal 5. Therefore, the area of one face of the cube is:
5 × 5 = 25
Since a cube has 6 equal faces, its surface area will be:
6 × 25 = 150
19. ?% of 60 = 24

1. 40
2. 48
3. 45
4. 42
5. 38
?% × 60 = 24
$$? = {24 \over 60} × 100$$ = 40
20. 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