The average of two numbers is 103. If 2 is added to the greater number, then the ratio of this number to the smaller number becomes 8 : 5. What is the greater number?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 126
The average gives the sum of the two numbers, and the ratio splits that sum, once 2 is added to it, into parts.
Sum of the two numbers: \(2\times103=206\)
After 2 is added to the greater number, the sum becomes \(206+2=208\), shared in the ratio 8 : 5
\(8+5=13\) parts \(=208\), so one part \(=16\)
Greater number \(+\,2=8\times16=128\), so the greater number is 126 (and the smaller is \(5\times16=80\))