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There are three constituencies A, B and C. The percentage amounts of males to the total voters in constituencies A, B, C and all three constituencies together are 55, 45, 60 and 52 respectively. If the percentage amounts of women in constituencies B to the total number of women in all three constituencies is 51.5625 respectively. What is the ratio of number of voters in constituency A, B and C?

There are three constituencies A, B and C. The percentage amounts of males to the total voters in constituencies A, B, C and all three constituencies together are 55, 45, 60 and 52 respectively. If the percentage amounts of women in constituencies B to the total number of women in all three constituencies is 51.5625 respectively. What is the ratio of number of voters in constituency A, B and C? Correct Answer 6 ∶ 5 ∶ 9

Let the total number of voters in constituencies A, B and C be a, b and c respectively

Total number of male voters in A = 55/100 × a = 0.55a

Total number of female voters in A = a – 0.55a = 0.45a

Total number of male voters in B = 45/100 × b = 0.45b

Total number of female voters in B = b – 0.45b = 0.55b

Total number of male voters in C = 60/100 × c = 0.6c

Total number of female voters in A = c – 0.6c = 0.4c

Total number of males = 0.55a + 0.45b + 0.6c = 52% of total voters

0.55a + 0.45b + 0.6c = 52/100 × (a + b + c)

0.55a + 0.45b + 0.6c = 0.52a + 0.52b + 0.52c

0.03a + 0.08c = 0.07b

3a + 8c = 7b      ---- 1

8c = 7b – 3a

c = (7b – 3a) /8

% number of females in B to total number of women = 0.55b/ (0.45a + 0.55b + 0.4c) × 100

51.5625 = 0.55b/ (0.45a + 0.55b + 0.4c) × 100      ---- 2

⇒ 23.203125a + 28.359375b + 20.625c = 55b

⇒ 23.203125a + 20.625c = 26.640625b × 64

⇒ 1485a + 1320c = 1705b

⇒ 1485a + 1320 (7b – 3a) /8 = 1705b

⇒ 990a = 550b

⇒ 9a = 5b

⇒ b = 1.8a

⇒ c = (7b – 3a) /8 = 1.2a

⇒ a : b : c = a : 1.8a : 1.2a

⇒ 5 : 9 : 6

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