Question 54

A son's present age is two-fifths of his mother’s age. After 8 years, he will be one half hismother's age. Whatis his mother's age now?

Solution

Assume mother's present age be 5x

then son's present age is two-fifth of mothers age that is $$ 2 \div 5 \times 5x =2x $$

Ratio of mother's age to son's age is 5x : 2x

After 8 years ratio becomes 5x+8 : 2x+8

after 8 years son's age will be one half of mothers age (Given)

that is, $$ 2x+8 = 1 \div 2 \times ( 5x+8) $$

Solving we get x=8

thus present age of mother $$ 5 \times 8= 40 $$

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