Question

dgo, the product of their
ages in years was 48.
.
[NCERT]
6. A girl is twice as old as her sister. Four years hence, the product of their ages (in
years) will be 160. Find their present ages.
[CBSE 2010]​

Answer 1

Answer:

The present ages of girl and her sister are 12 and 6 years respectively.

Step-by-step explanation:

=> Let the present age of her sister be x.

=> Then, the age of girl be 2x.

After 4 years,

=>the age of a girl be 2x + 4.

=>and her sister's age be x + 4.

According to the question,

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

=> 2x^2 + 4x + 8x + 16 = 160

=> 2x^2 + 12x + 16 -160 = 0

=>2x^2 + 12x - 144 = 0

=> 2( x^2 + 6x - 72 ) = 0

=>x^2 + 6x - 72 = 0/2

=> x^2 + 12x - 6x - 72 = 0

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

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

=> x + 12 = 0 and x - 6 = 0

Therefore, x = -12 and x = 6

=> Age cannot be negative.

Since, x = 6.

=> 2x = 2 * 6 = 12

Therefore, the ages of a girl and her sister are 12 and 6 years respectively.