Two numbers are in the ratio 3 : 5. If 3 is subtracted from the first number and 3 is added to the second number, the ratio becomes 1 : 3. The sum of the numbers is?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 24
Numbers in the ratio 3 : 5 can be written as \(3k\) and \(5k\) for some number \(k\); the changed numbers then give one equation in \(k\).
After the change: \(\displaystyle \frac{3k-3}{5k+3}=\frac{1}{3}\)
\(9k-9=5k+3\)
\(4k=12\), so \(k=3\)
The numbers are 9 and 15, and their sum is 24