Samartha is five times as old as his daughter Trisha and Samartha’s wife Phalguni’s age is 26 years more than that of Trisha. The difference between thrice the age of Samarth ten years ago and twice the age of Phalguni ten years ago was 42 years. What will be the respective ratio of Phalguni’s age 12 years hence and Samartha’s age 12 years hence?
Solution
Let Trisha's present age = $$x$$ years
=> Samartha's present age = $$5x$$ years
Phalguni's present age = $$(x + 26)$$ years
Acc. to ques, => $$3 (5x - 10) - 2 (x + 26 - 10) = 42$$
=> $$15x - 30 - 2x - 32 = 42$$
=> $$13x = 42 + 62 = 104$$
=> $$x = \frac{104}{13} = 8$$
Thus, after 12 years :
Phalguni's age = $$x + 26 + 12 = 8 + 38 = 46$$ years
Samartha's age = $$5x + 12 = 5(8) + 12 = 52$$ years
$$\therefore$$ Required ratio = $$46 : 52 = 23 : 26$$
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