Discussion :: Problems on Ages

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.
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 
Answer : Option C
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.\(\frac { D10} { S10 }\)=\(\frac { 3} { 1 }\)....(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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