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
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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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