Question : The two numbers are in the ratio of 5 : 3. If 9 is subtracted from each, then the new ratio is 9 : 5. What are the two numbers?
Option 1: 50 and 30
Option 2: 45 and 27
Option 3: 90 and 54
Option 4: 15 and 45
Correct Answer: 90 and 54
Solution :
Let the numbers be $5x$ and $3x$
According to the question,
$\frac{5x–9}{3x–9} = \frac{9}{5}$
⇒ $25x–45 = 27x–81$
⇒ $36 = 2x$
⇒ $x = \frac{36}{2}$
⇒ $x = 18$
Thus, the numbers are $(5 × 18) = 90$ and $(3 × 18) = 54$
Hence, the correct answers are 90 and 54.
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