Solved Examples Set 3 (Quantitative Ability)

1. 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

2. How much would I have to pay for a book which cost $ 72 to product, if the printing company sold it to a bookseller at 20% profit and in return the bookseller sold it to me at a profit of 25%?

   1. $ 104
   2. $ 106
   3. $ 108
   4. $ 110
   5. $ 109

   Cost of the book product = $ 72
   Profit of printing company = 20% of 72 = 0.2 x 72 = 14.4
   Now the cost of the book = 72 +14.4 = $ 86.4
   Profit of the bookseller = 25% of 86.4 = 21.4
   Finally, the cost of the book = 86.4 + 21.4 = $ 108

3. 40 arithmetic questions, each carrying equal marks, were given in a class test. A boy answered 25 questions correctly. What percentage was this? To pass a test a student must answer at least 45% of the questions correctly. Find the least number of correct answers needed to pass.

   1. 62.5%, 18
   2. 63.5%, 16
   3. 64.5%, 20
   4. 61.0%, 21
   5. 60.0%, 22

   \(x \text{% of } 40 = 25\)
   \(x \text{% } × 40 = 25\)
   \(x = {25 \over 40} × 100 \)
   x = 62.5
   
   \(x = 45 \text{% of } 40 \)
   \(x = 0.45 × 40 \)
   x = 18

4. 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

5. A man was 32 years old when his daughter was born. He is now five times as old as his daughter. How old is his daughter now?

   1. 7 years
   2. 8 years
   3. 9 years
   4. 10 years
   5. 6 years

   Let's assume the daughter is d years old now. That means that the man is now (32 + d) years old, so that
   (32 + d) = 5d
   32 = 4d
   d = 8

6. 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

7. 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

8. Which of the following is the largest?

   1. half of 30% of 280
   2. one-third of 70% of 160
   3. twice 50% of 30
   4. three times 40% of 40
   5. 60% of 60

   Let us calculate the value of each:
   A. 0.5 × 0.3 × 280 = 42
   B. 0.33 × 0.7 × 160 = 36.96
   C. 2 × 0.5 × 30 = 30
   D. 3 × 0.4 × 40 = 48
   E. 0.6 × 60 = 36

9. A rectangular room is 6 m long, 5 m wide and 4 m high. The total volume of the room in cubic meters is

   1. 24
   2. 30
   3. 120
   4. 240
   5. 140

   Total volume = length × width × height = 6 × 5 × 4 = 120

10. \( {𝑥 - 8 \over 24} = {3 \over 4} \)
    What is the value of 𝑥 in the equation?

    1. 10
    2. 20
    3. 26
    4. 31
    5. 40

    By cross multiplying, 4(𝑥 – 8) =3 × 24. Thus, 4𝑥 – 32 = 72, and so 4𝑥 = 104 and 𝑥 = 26.

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. \( {63.84 \over ?} \) = 21

    1. 3.04
    2. 3.4
    3. 30.4
    4. 300.4
    5. 0.304

    ? = \( 63.84 \over 21 \) = 3.04

13. \( {1250 \over 25} × 0.5 = ? \)

    1. 250
    2. 50
    3. 2.5
    4. 25
    5. 125

    \( {1250 \over 25} × 0.5 = 50 × 0.5 = 25 \)

14. 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

15. \( {0.027 \over 90} = ? \)

    1. 0.0003
    2. 0.03
    3. 3
    4. 0.00003
    5. 0.003

    \( {0.027 \over 90} = {27 \over 1000 × 90} = {3 \over 10000} = 0.0003 \)

16. 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

17. 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

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 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

20. 
    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

Solved Examples Set 1
Solved Examples Set 2
Solved Examples Set 3