Question

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 1

Hint: In this question Divya is twice as old as Shruti. And it is asked about their ages difference. The ratio of their ages would $ 9:5 $ respectively after $ 5 $ years. And their age’s ratio was $ 3:1 $ respectively $ 10 $ years back. To solve this question let the proportional quantity be $ x $ and proceed it.

Complete step-by-step answer:
Given: Divya is twice as old as Shruti
Five years hence the ratio of their ages would be $ 9:5 $
Ten years back the ratio of their ages was $ 3:1 $
For solving the question first of all we assume the age of the Shruti be $ x $ years
So, age of Divya $ =2x $ years
Now, according to first condition, five years hence,
The age of Shruti $ =x+5 $ years
The age of Divya $ =2x+5 $ years
And their age ratio is given so,
 $
 \Rightarrow \dfrac{2x+5}{x+5}=\dfrac{9}{5} \\
\Rightarrow 10x+25=9x+45 \\
\Rightarrow x=45-25 \\
\Rightarrow x=20\,years \\
 $
Hence, Shruti’s age is $ 20 $ years
So, Divya age is $ 40 $ years
Hence, alone condition I is enough to find out the answer now try II condition
Now, Ten years back
The age of Shruti = $ x-10 $ years
The age of Divya = $ 2x-10 $ years
Their age ratio is given
 $
 \Rightarrow \dfrac{2x-10}{x-10}=\dfrac{3}{1} \\
\Rightarrow 2x-10=3x-30 \\
\Rightarrow 2x-3x=-30+10 \\
\Rightarrow -x=-20 \\
\Rightarrow x=20\,years \\
 $
Shruti’s age is $ 20 $ years
So, Divya age is $ 40 $ years
Hence, condition II is also sufficient to find out the result.
So, option C either I or II alone is sufficient to answer.
So, the correct answer is “Option C”.

Note: In the question, we have to check one by one each condition and when we assume Shruti’s age then be careful to put the age ratio carefully otherwise it will lead to wrong answers. Don't check only one option because options that are given have the requirement of checking both conditions.