Question
Eight years ago, the ratio of the ages of A and B was 3
: 5. The sum of their present ages is 56 years. What is the present age of the younger person?Solution
Let present ages of A and B be a and b. 8 years ago: (a − 8) : (b − 8) = 3 : 5 So, (a − 8)/(b − 8) = 3/5 ⇒ 5(a − 8) = 3(b − 8) ⇒ 5a − 40 = 3b − 24 ⇒ 5a − 3b = 16 …(i) Also, a + b = 56 …(ii) From (ii), a = 56 − b. Substitute in (i): 5(56 − b) − 3b = 16 280 − 5b − 3b = 16 280 − 8b = 16 8b = 264 b = 33 Then a + b = 56 ⇒ a = 23. Younger person = 23 years.
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