Question

By how many years is Rasika younger Alan her brother Sunil?
I. The ratio between Rasika's present age and Sunil's age after four years is 5: 7 respectively.
II. The ratio between Rasika's age four years ago age and Sunil's present age is 2: 3 respectively.

• A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
• B. If the data in the statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
• C. If the data either in statement I alone or in statement II alone is sufficient to answer the question.
• D. If the data in both the statements I and II together is not sufficient to answer the question.
• E. If the data in both the statements I and II together are necessary to answer the question.

Answer 1

The correct option is E If the data in both the statements I and II together are necessary to answer the question.

Rasika's present age : (Sunil's present + 4)
= 5 : 7 . . . .(i)
Rasika's age - 4 : Sunil's present age
= 2 : 3 . . . (ii)
$\frac{R}{S+4}=\frac{5}{7}$
7R = 5S + 20
7R - 5S = 20 . . . (i)
$\frac{R-4}{S}=\frac{2}{3}$
3R - 12 = 2S
3R = 2S + 12 . . . .(ii)
By solving Eqs. (i) and (ii), we get
R = 20
and S = 24
$\therefore$ Rasika is 4 years younger than her brother Sunil