Question

The present age of Mohan's mother is four times that of Mohan's age. Mohan's age ten years from now will be<br />one third of his mother's present age. What are their present ages?<br />​

Answer 1

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Answer 2

The present age of Mohan's mother is four times that of Mohan's age.

Mohan's age ten years from now will be  one third of his mother's present age.

$\Large{\underline{\underline{\red{GiVen:-}}}}$

The present ages of Mohan and his mother.

$\Large{\underline{\underline{\green{SoLuTioN:-}}}}$

Let the present age of Mohan be x and the present age of Mohan's mother be y.

According to the question,

CASE - 1

$\sf{y=4x}$      . . .(i)

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CASE - 2

$\sf{x+10=\dfrac{1}{3}\times (y+10) }$

Substituting value of y from (i) :-

$\longmapsto \sf{x+10=\dfrac{1}{3}\times (4x+10) }$

$\longmapsto \sf{3(x+10)=4x+10}$

$\longmapsto \sf{3x+30=4x+10}$

$\longmapsto \sf{30-10=4x-3x}$

$\longmapsto \sf{20=x}$

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Therefore,

the present age of Mohan = x = 20 years.

The present age of Mohan's mother = y = 4x = 4 × 20 = 80 years.