Question
The present ages of Priya’s father and mother are in
the ratio R:S. If the father’s age increases by 4 years and the mother’s age decreases by 4 years, the ratio becomes 13/7. If the sum of their actual ages is 80 years, find the father’s current age.Solution
ATQ, Father’s age = x Mother’s age = y x + y = 80 — (1) (x + 4) / (y − 4) = 13 / 7 7(x + 4) = 13(y − 4) 7x + 28 = 13y − 52 7x − 13y = −80 — (2) Multiply (1) by 13: 13x + 13y = 1040 Add with (2): (13x + 13y) + (7x − 13y) = 1040 − 80 20x = 960 x = 960 / 20 = 48 Required answer = 48 years
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