Two numbers are in the ratio 3 : 5. If 10 is added to each number, then the ratio becomes 5 : 7. Find the numbers.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 15, 25
Numbers in the ratio 3 : 5 can be written as \(3k\) and \(5k\); adding 10 to each gives the new ratio, which fixes the common multiplier \(k\).
After adding 10 to each: \(\displaystyle\frac{3k+10}{5k+10}=\frac{5}{7}\)
\(21k+70=25k+50\)
\(4k=20\), so \(k=5\)
The numbers are \(3\times5=15\) and \(5\times5=25\)