A man’s age exceeds that of his wife by 6 years. 10 years ago, the ratio of their ages was 5 : 4. Find the present age of the man.
Question
A man’s age exceeds that of his wife by 6 years. 10 years ago, the ratio of their ages was 5 : 4. Find the present age of the man.
Solution
Let's denote the man's current age as M and the woman's current age as W.
From the problem, we know two things:
- M = W + 6 (The man’s age exceeds that of his wife by 6 years)
- (M - 10) / (W - 10) = 5/4 (10 years ago, the ratio of their ages was 5 : 4)
We can substitute the first equation into the second to solve for one of the variables.
Substituting M from the first equation into the second equation, we get:
(W + 6 - 10) / (W - 10) = 5/4 (W - 4) / (W - 10) = 5/4
Cross-multiplying to clear the fraction gives us:
4(W - 4) = 5(W - 10) 4W - 16 = 5W - 50
Solving for W, we get:
W = 34
Substituting W = 34 into the first equation, we get:
M = 34 + 6 = 40
So, the man is currently 40 years old.
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