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

# Solved Examples Set 1 (Quantitative Ability)

1. ? × 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
2. 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
3. A and B enter into a partnership contributing $800 and$ 1000 respectively. At the end of 6 months they admit C, who contributes $600. After 3 years they get a profit of$ 966. Find the share of each partner in the profit.

1. $336,$ 420, $210 2.$ 360, $400,$ 206
3. $380,$ 390, $196 4.$ 345, $405,$ 210
5. $325,$ 400, $200 A shares = 800 × 3 = 2400 B shares = 1000 × 3 = 3000 C shares = 600 × 2 1⁄2 = 1500 Total shares = 2400 + 3000 + 1500 = 6900 A's profit = $$2400 \over 6900$$ × 966 =$ 336
B's profit = $$3000 \over 6900$$ × 966 = $420 C's profit = $$1500 \over 6900$$ × 966 =$ 210
4. A basket that contains 2 apples, 3 bananas, 6 oranges, and 4 pears is in the workroom. When Ms. Hutchinson went to the workroom, other workers had already taken 1 banana, 2 oranges, and 1 pear. From the remaining fruit, Ms. Hutchinson randomly took 3 pieces of fruit separately from the basket. If each fruit is equally likely to be chosen, what is the probability that the third piece was an orange if the first two she took were also oranges?

1. 4/165
2. 9/11
3. 4/11
4. 3/11
5. 2/9
Ms. Hutchinson randomly takes the 3 pieces of fruit from the basket, there are 2 apples, 3 -1 = 2 bananas, 6 - 2 = 4 oranges, and 4 - 1 = 3 pears. Assuming that the first 2 pieces of fruit Ms. Hutchinson takes are oranges, there will be 2 apples, 2 bananas, 4 - 2 = 2 oranges, and 3 pears left in the basket when she selects the third piece of fruit. The probability that the third piece of fruit she selects will be an orange is $$\frac{2}{2 + 2 + 2 + 3} = \frac{2}{9}$$.
5. 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
6. 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
7. 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
8. 72 + 679 + 1439 + 537+ ? = 4036

1. 1309
2. 1208
3. 2308
4. 2423
5. 1309
72 + 679 + 1439 + 537+ ? = 4036
2727 + ? = 4036
? = 4036 - 2727 = 1309
9. A can do a piece of work in 10 days and B can do it in 15 days. The number of days required by them to finish it, working together is

1. 8
2. 7
3. 6
4. 4
5. 3
A's 1 day work = $$1 \over 10$$
B's 1 day work = $$1 \over 15$$
Now both A and B's 1 day work = $${1 \over 10} + {1 \over 15}$$ = $$3 + 2 \over 30$$ = $$1 \over 6$$
Hence the work by both A and B will be completed in 6 days.
10. $${63.84 \over ?}$$ = 21

1. 3.04
2. 3.4
3. 30.4
4. 300.4
5. 0.304
? = $$63.84 \over 21$$ = 3.04
11. 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.
12. 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
13. A certain number was doubled and the result then multiplied by 3. If the product was 138, find the number.

1. 21
2. 23
3. 25
4. 27
5. 19
Let x be the number
the number is doubled, 2x
the result is multiplied by 3, 3 × 2x = 6x
6x = 138
x = $$138 \over 6$$ = 23
14. A fruit-seller has 120 oranges. Given that he has 20% more apples than oranges and 40% less oranges than pears, find the number of apples and the number of pears the fruit seller has.

1. 144, 200
2. 148, 380
3. 149, 220
4. 140, 190
5. 142, 190
No. of apples = 120 + 20% of 120 = 120 + 0.2 × 120 = 144

Let x = No. of pears
x - 40% of x = 120
x - 0.4x = 120
0.6x = 120
x = $$120 \over 0.6$$ = 200
Hence, no. of pears = 200
15. $$\frac{\frac{7}{10} × 14 × 5 × \frac{1}{28}}{\frac{10}{17} × \frac{3}{5} × \frac{1}{6} × 17} =$$

1. 4/7
2. 1
3. 7/4
4. 2
5. 17/4

16. $$25 \text{% of }{4 \over 4\text{%}} \text{ of }{1 \over 25} = ?$$

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
17. 8 : ? :: 1 : 4

1. 24
2. 16
3. 0
4. 32
5. 20
? × 1 = 8 × 4
? = 32
18. 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%
19. 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.
20. 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