Question

The difference of the ages of a sister and her younger brother is 6 years. The
numerical value of the product of their ages is equal 4 times the sum of their ages.
Find the present ages of the sister and her brother.
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Answer 1

Answer:

The present age of the sister is 12 years and her brother is 6 years.

Explanation:

Let the present age of the sister and her brother be (x + 6) and x, respectively

Now {x ×( x + 6)} = 4 (2x + 6)

> x2 + 6x = 8x + 24

> x2 - 2x - 24 = 0

> x2 - 6x + 4x - 24 = 0

> x(x - 6) + 4 (x - 6)

>(x + 4)(x - 6)

Therefore, x = 6 , as -4 can't practically be anyone's age

Hence, The present age of the sister is 12 years and her brother is 6 years.