Question : A number is divided in the ratio 5 : 7. When 6 is added to each, the ratio changes to 7 : 9. Find the greater number.
Option 1: 12
Option 2: 18
Option 3: 15
Option 4: 21
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Correct Answer: 21
Solution : Let the numbers be $5x$ and $7x$. According to the question, $\frac{5x+6}{7x+6}=\frac{7}{9}$ ⇒ $45x+54=49x+42$ ⇒ $4x=12$ ⇒ $x=3$ Thus, the greater number is $7x=7\times3=21$ Hence, the correct answer is 21.
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