Question : The ratio of the ages of the father and the mother was 11 : 10 when their son was born. The ratio of ages of the father and the mother will be 19 : 18 when the son will be twice his present age. What is the ratio of the present ages of the father and the mother?
Option 1: 15 : 14
Option 2: 14 : 13
Option 3: 16 : 15
Option 4: 17 : 16
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Correct Answer: 15 : 14
Solution :
Given:
The ratio of ages of the father and the mother when their son is born = 11 : 10.
Let the father and the mother's ages be 11k and 10k, respectively, when their son is born.
And the ratio of their ages will be 19 : 18 when the son is twice his present age.
Let the present age of the son be $x$ years.
Twice that age is $2x$ years.
The father and the mother's present ages become 11k + x and 10k + x, respectively.
According to the given information,
⇒ $\frac{11k+2x}{10k+2x}=\frac{19}{18}$
⇒ $18(11k+2x)=19(10k+2x)$
⇒ $198k+36x=190k+38x$
⇒ $8k=2x$
⇒ $x=4k$
Now,
The ratio of the present ages of the father and the mother will be
⇒ $\frac{11k+x}{10k+x}=\frac{11k+4k}{10k+4k}$ = $\frac{15}{14}$
So, the required ratio is = 15 : 14
Hence, the correct answer is 15 : 14.
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