Question : Two numbers are in the ratio 9 : 16. If both numbers are increased by 40, then their ratio becomes 2 : 3. What is the difference between the two numbers?
Option 1: 64
Option 2: 60
Option 3: 48
Option 4: 56
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Correct Answer: 56
Solution : Let the two numbers as $9x$ and $16x$. According to the problem, if both numbers are increased by 40, their ratio becomes 2 : 3. $⇒\frac{9x + 40}{16x + 40} = \frac{2}{3}$ $⇒27x + 120 = 32x + 80$ $⇒5x = 40$ $⇒x = 8$ So, the two numbers are: $⇒9x = 9 \times 8 = 72$ $⇒16x = 16 \times8 = 128$ The difference between the two numbers = 128 – 72 = 56 Hence, the correct answer is 56.
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