Question

Kishore is two years older than Rakesh if four years ago the product of their age was 120 then find their present age

Answer 1

Answer:

Rakesh is 16 years old and Kishore is 18 years old .

Step-by-step explanation:

Let ,

Rakesh's age be x

Then , Kishore's age will be ( x + 2 )

A/Q ,

4 years ago ,

( x - 4 ){ ( x - 2 ) - 4 } = 120

= ( x - 4 ) ( x - 2 - 4 ) = 120

= ( x - 4 ) ( x - 6 ) = 120

= x ( x - 6 ) - 4 ( x - 6 ) = 120

= x^2 - 6x - 4x + 24 = 120

= x^2 - 10x + 24 = 120

= x^2 - 10x = 120 - 24

= x^2 - 10x = 96

= x^2 - 10x - 96 = 0

= x^2 - 16x + 6x - 96 = 0 [ splitting mid term ]

= x ( x - 16 ) + 6 ( x - 16 ) = 0

= ( x + 6 ) ( x - 16 ) = 0

Therefore ,

x = -6 & x = 16

Now , since age cannot be a negative number , therefore we consider the value of x to be 16 .

Hence , Rakesh's age is 16 years

and Kishore's age is ( x + 2 ) = 16 + 2 = 18 years .