The average of two numbers is 56. If 4 is added to the smaller number, then the ratio of the new number to the other number is 1: 3. What is the smaller number?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 25
The average of two numbers gives their sum (average \(\times\) 2), so the larger number can be written in terms of the smaller one. The ratio then gives one equation in the smaller number.
Sum of the two numbers: \(2\times56=112\); let the smaller be \(x\), so the other is \(112-x\)
Ratio after adding 4 to the smaller: \(\displaystyle\frac{x+4}{112-x}=\frac{1}{3}\)
The ratio as an equation: \(3(x+4)=112-x\), so \(4x=100\)
The smaller number is \(x=25\)