Question

the difference between two sosters age is 5 and 10 years ageo if the elder one was twice as old as younger one .find their present age.

Answer 1

Let the ages of the sisters at present be x and x + 5

Ten years ago, their age was x - 10, x - 5

hence:

x - 5 = 2(x - 10)

=> x - 5 = 2x - 20

=> x - 2x = -20 + 5

=> -x = - 15

x = 15

hence their present ages are 15 and 20

Answer 2

Let the present age of both the sisters be S1 and S2.

According to the question the difference of the age of the two sisters is 5 i.e. S1 - S2 is equal to 5.

Now 10 years ago their age should be as S1 - 10 and S2 - 10 respectively.

Also it was said that,

S1 - 10 = 2 * (S2 - 10)

or, S1 - 10 = 2S2 - 20

or, S1 - 2S2 = -10

Also, we have S1 - S2 = 5; S2 = S1 - 5

or, S1 - 2(S1 - 5) = -10

or, -S1 = -20

or, S1 = 20. S2 = 15.

Therefore, their present ages are 20 and 15. [Ans]