Rs. 78 is divided among 7 men, 11 women and 5 boys so that each woman may have thrice as much as a boy and as much as a man and a boy together. Find the share of a man?
Solution
Correct Answer: Option B
Say M is the share of a man, W is the share of a woman and B is the share of a boy.
⇒ W = 3 × B …… Eq.1
W = B + M …… Eq.2
7M + 11W + 5B = 78 …… Eq.3
From Eq.1 and Eq.2
We get, 3B = B + M
⇒ M = 2B
Substitute M = 2B in Eq.3
⇒ 14B + 11W + 5B =78
⇒ 11W + 19B = 78
Put W = 3B
⇒ (11 × 3 + 19) × B = 78
B = 78/52 = Rs.1.50
W = 3 × 1.50 = Rs.4.50
From Eq.2
We get, M = W – B = 4.50 – 1.50 = Rs.3.00
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