Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

A. 16 years

B. 18 years

C. 28 years

D. 24.5 years

E. None of these

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{Rahul's}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}. \cr & {\text{Then,}}\,{\text{Sachin's}}\,{\text{age}} = \left( {x - 7} \right)\,{\text{years}}. \cr & \therefore \frac{{x - 7}}{x} = \frac{7}{9} \cr & \Rightarrow 9x - 63 = 7x \cr & \Rightarrow 2x = 63 \cr & \Rightarrow x = 31.5 \cr & {\text{Hence,}}\,{\text{Sachin's}}\,{\text{age}} \cr & = \left( {x - 7} \right)\,{\text{years}} \cr & = 24.5\,{\text{years}} \cr} $$