Question : The ratio of present ages of Neelam and Rajni is 6 : 5. After six years, their ages will be in the ratio of 13 : 11. What is the present age of Rajni?
Option 1: 45 years
Option 2: 75 years
Option 3: 30 years
Option 4: 60 years
Correct Answer: 60 years
Solution :
Given: The ratio of present ages of Neelam and Rajni is 6 : 5.
After six years, their ages will be in the ratio of 13 : 11.
Let the present ages of Neelam and Rajni be $6x$ and $5x$.
According to the question,
$\frac{6x+6}{5x+6}=\frac{13}{11}$
⇒ $66x+66=65x+78$
⇒ $66x-65x=78-66$
⇒ $x=12$
The present age of Rajni = $5x=12\times 5=60$ years
Hence, the correct answer is 60 years.
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