The ratio of the ages of the father and mothe | vedclass

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(A) Let the present age of the son be $S$ years.When the son was born,the age of the son was $0$. Let the father's age be $11x$ and the mother's age b

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$15: 14$

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(A) Let the present age of the son be $S$ years.When the son was born,the age of the son was $0$. Let the father's age be $11x$ and the mother's age be $10x$ at that time.Since the son was born $S$ years ago,the present ages of the father and mother are $(11x + S)$ and $(10x + S)$ respectively.When the son is twice his present age,his age will be $2S$. This will happen $S$ years from now.At that time,the father's age will be $(11x + S + S) = 11x + 2S$ and the mother's age will be $(10x + S + S) = 10x + 2S$.According to the problem,the ratio at that time is $19: 18$:$\frac{11x + 2S}{10x + 2S} = \frac{19}{18}$$18(11x + 2S) = 19(10x + 2S)$$198x + 36S = 190x + 38S$$8x = 2S \implies S = 4x$Now,substitute $S = 4x$ into the expressions for present ages:Father's present age $= 11x + 4x = 15x$Mother's present age $= 10x + 4x = 14x$The ratio of their present ages is $\frac{15x}{14x} = 15: 14$.

The ratio of the ages of the father and mother was $11: 10$ when their son was born. The ratio of the ages of the father and mother will be $19: 18$ when the son is twice his present age. What is the ratio of the present ages of the father and mother?

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