Question : Directions: The present ages of Vikas and Sujit are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Sujit's present age in years?
Option 1: 6
Option 2: 24
Option 3: 18
Option 4: 27
Correct Answer: 24
Solution :
Given:
The present ages of Vikas and Sujit are in the ratio of 5 : 4
⇒ Present age of Vikas = 5 × A
⇒ Present age of Sujit = 4 × A
Age of Vikas after 3 years = (5 × A) + 3
Age of Sujit after 3 years = (4 × A) + 3
The ratio of their ages after 3 years is 11 : 9
⇒ $\frac{(5\times A)\:+\: 3}{(4\times A)\:+\: 3}=\frac{11}{9}$
⇒ 9 × ((5 × A) + 3) = 11 × ((4 × A) + 3)
⇒ (45 × A) + 27 = (44 × A) + 33
⇒ A = 6 years
Therefore, Sujit's present age = 4 × A = 4 × 6 = 24 years.
Hence, the second option is correct.
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