Question

3. A girl is twice as old her sister. Four years hence,
the product of their ages (in years) will be 160. Find
the her present age.​

Answer 1

Answer:

Let the age of the sister be x, so girl's age = 2x.

After 4 years,

age of sister = x+4

age of girl = 2x +4

According to the question,

(x+4)(2x+4) = 160

=> x(2x) + 4(2x) + x(4) + 4(4) = 160

=> 2x² + 8x + 4x + 16 - 160 = 0

=> 2x² + 12x - 144 = 0

=> 2(x² + 6x - 72)/2 = 0/2

=> x² + 6x -72 = 0

=> x² + 12x - 6x -72 = 0

=> x (x+12) - 6(x+12) = 0

=> (x+12) (x-6) = 0

=> x = -12 or x= +6

Since age can't be negative,

=> x = 6

=> age is sister = 6

=> age of the girl = 2×6 = 12 years

Hence, our answer is 12 years.