The ratio between two numbers is 2 : 3. If each number is increased by 2, then the ratio becomes 3 : 4. Find the sum of the original numbers.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10
Numbers in the ratio 2 : 3 can be written as \(2x\) and \(3x\). Adding 2 to each gives a new ratio, which fixes \(x\).
After adding 2 to each: \(\displaystyle\frac{2x+2}{3x+2}=\frac{3}{4}\)
\(4(2x+2)=3(3x+2)\) gives \(8x+8=9x+6\), so \(x=2\)
The numbers are 4 and 6, and their sum is \(4+6=10\)