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### Discussion :: Problems on Ages

1.  Divya is twice as old as Shruti. What is the difference in their ages? I. Five years hence, the ratio of their ages would be 9 : 5. II. Ten years back, the ratio of their ages was 3 : 1.
2.  A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer E. Both I and II are necessary to answer

Explanation :

Let Divya's present age be D years and Shruti's present age b S years

Then, D = 2 x S        D - 2S = 0 ....(i)

I.$$\frac { D+5} { S+5 }$$=$$\frac {9} { 5 }$$....(ii)

II.$$\frac { D-10} { S-10 }$$=$$\frac { 3} { 1 }$$....(iii)

From (ii), we get : 5D + 25 = 9S + 45        5D - 9S = 20 ....(iv)

From (iii), we get : D - 10 = 3S - 30        D - 3S = -20 ....(v)

Thus, from (i) and (ii), we get the answer.

Also, from (i) and (iii), we get the answer.

I alone as well as II alone give the answer. Hence, the correct answer is (C).

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