Worksheet on Ratio and Proportion

Solved Questions on Ratio and Proportions

1. The earning of Charlie is $83400 per year and the earning of Harry is $6250 every month. If the monthly expenses of both Charlie and Harry are around $5210. What is the ratio of their savings?

a) 50 : 87
b) 52 : 87
c) 87 : 50
d) 87 : 52

Answer: d) 87 : 52

Explanation: Income of Charlie per year = $83400
Income of Charlie per month = $83400/12 = $6950
Savings of Charlie per month = $(6950 − 5210) = $1740
Income of Harry per year = $6250
Savings of Harry per month = $(6250 − 5210) = $1040

Ratio of savings of Charlie and Harry = $1740 : $1040 = 87 : 52

2. In a club of 360 members, 96 like to play table tennis, 144 like to play badminton, 40 like to play cribbage and the remaining like to play volleyball. If a player is not playing two games or more, what is the ratio of the number of members who like to play volleyball to badminton?

a) 5 : 9
b) 5 : 7
c) 7 : 5
d) 9 : 5

Answer: a) 5 : 9

Explanation: Total members in a club = 360 members
Members who like to play table tennis = 96 members
Members who like to play badminton = 144 members
Members who like to play carrom = 40 members
Members who like to play volleyball = 360 – (96 + 144 + 40)
                                                     = 360 – 280
                                                      = 80 members

Ratio of the number of members who like to play volleyball to badminton = 80 : 144
                                                                                                           =  5 : 9  

3. What is the third proportional to 5.25 and 7?

a) 3¹⁄₃
b) 3²⁄₃
c) 9¹⁄₃
d) 9²⁄₃

Answer: c) 9¹⁄₃

Explanation:

4. What is the ratio a : b if 5a + 2b : 3b − 5a :: 5 : 2?

a) 11 : 35
b) 35 : 11
c) 13 : 35
d) 35 : 13

Answer: a) 11 : 35

Explanation: 5a + 2b : 3b − 5a :: 5 : 2
⇒ 5a + 2b3b − 5a = 52
⇒ 2 × (5a + 2b) = 5 × (3b − 5a)
⇒ 10a + 4b = 15b − 25a
⇒ 10a + 25a = 15b − 4b
⇒ 35a = 11b
⇒ ab = 1135
⇒ a : b = 11 : 35

5. There are a few building blocks in the box that have the names P, Q, R and S written on them. The ratio of blocks P : Q : R : S is in the ratio 13 : 3 : 11 : 7. What is the number of ‘R’ blocks if the number of ‘Q’ blocks is 144 less than the number of ‘S’ blocks?

a) 336
b) 396
c) 468
d) 486

Answer: b) 396

Explanation: 

Let the number of the blocks P : Q : R : S be 13x, 3x, 11x and 7x, respectively.

Number of ‘Q’ blocks is 144 less than the number of ‘S’ blocks.
⇒ 3x = 7x − 144
⇒ 7x − 3x = 144
⇒ 4x = 144
⇒ x = 36

Number of ‘R’ blocks = 11× x
                                = 11 × 3
                                 = 396