Subject: General Aptitude · Chapter: Problems on Ages · Exam: · Marks: · Difficulty:
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.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
Let Divya's present age be D years and Shruti's present age be S years. Then, $\mathrm{D}=2\times\mathrm{S} \Leftrightarrow \mathrm{D}-2\mathrm{S}=0$. I. $\frac{\mathrm{D}+5}{\mathrm{S}+5}=\frac{9}{5}$ II. $\frac{\mathrm{D}-10}{\mathrm{S}-10}=\frac{3}{1}$. From I, we get $5\mathrm{D}+25=9\mathrm{S}+45 \Leftrightarrow 5\mathrm{D}-9\mathrm{S}=20$. From II, we get $\mathrm{D}-10=3\mathrm{S}-30 \Leftrightarrow \mathrm{D}-3\mathrm{S}=-20$. Thus, D and S can be found from (D-2S=0) together with either I or II. I alone as well as II alone gives the answer. Correct answer is (c).
Explanation as extracted from the printed page; notation may be imperfect.