The product of Ramu’s age (in years) five years ago and his age (in years) nine years later is 15. Determine Ramu’s present age.

Given:

The product of Ramu’s age (in years) five years ago and his age (in years) nine years later is 15. 

To do:

We have to find Ramu's present age.

Solution:

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

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

The age of Ramu 9 years later$=x+9$ years.

According to the question,

$(x-5)(x+9)=15$

$x^2-5x+9x-45=15$

$x^2+4x-45-15=0$

$x^2+4x-60=0$

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

$x^2+10x-6x-60=0$

$x(x+10)-6(x+10)=0$

$(x+10)(x-6)=0$

$x+10=0$ or $x-6=0$

$x=-10$ or $x=6$

Age cannot be negative. Therefore, the value of $x$ is $6$.

The present age of Ramu is $6$ years.

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Updated on: 10-Oct-2022

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