The product of Shikha’s age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.

Given:

The product of Shikha’s age five years ago and her age 8 years later is 30, her age at both times being given in years.

To do:

We have to find her present age.

Solution:

Let the present age of Shikha be $x$ years.

This implies, the age of Shikha 5 years ago$=x-5$ years.

The age of Shikha 8 years later$=x+8$ years.

According to the question,

$(x-5)(x+8)=30$

$x^2-5x+8x-40=30$

$x^2+3x-40-30=0$

$x^2+3x-70=0$

Solving for $x$ by factorization method, we get,

$x^2+10x-7x-70=0$

$x(x+10)-7(x+10)=0$

$(x+10)(x-7)=0$

$x+10=0$ or $x-7=0$

$x=-10$ or $x=7$

Age cannot be negative. Therefore, the value of $x$ is $7$.

The present age of Shikha is $7$ years.

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Updated on: 10-Oct-2022

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