Question : The ratio of two numbers is 5 : 9. If 6 is added to the greater number and 6 is subtracted from the smaller number, the greater number becomes 6 times the smaller number. What are the numbers?
Option 1: 15 and 17
Option 2: 10 and 18
Option 3: 25 and 45
Option 4: 20 and 36
Correct Answer: 10 and 18
Solution :
Given: The ratio of two numbers is 5 : 9. If 6 is added to the greater number and 6 is subtracted from the smaller number, the greater number becomes 6 times the smaller number.
Let the greater number and the smaller number be 9$x$ and 5$x$ respectively.
According to the question,
$9x+6=6(5x-6)$
⇒ $30x-9x=36+6$
⇒ $x=\frac{42}{21}$
⇒ $x=2$
So, the numbers are (5 × 2) = 10 and (9 × 2) = 18
Hence, the correct answer is 10 and 18.
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