Question : Two numbers are in the ratio 12 : 7. If their HCF is 25, find the numbers.
Option 1: 225 and 135
Option 2: 300 and 175
Option 3: 300 and 50
Option 4: 175 and 120
Correct Answer: 300 and 175
Solution :
The numbers in the ratio 12 : 7 can be represented as $12x$ and $7x$, where $x$ is a common factor.
Given that their Highest Common Factor (HCF) is 25, we can say that $x = 25$.
Therefore, the two numbers are,
First number = $12x = 12 \times 25 = 300$
Second number = $7x = 7 \times 25 = 175$
Hence, the correct answer is 300 and 175.
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