The average of four numbers is 40. If the first number is one-third of the sum of the remaining numbers, then the first number is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 40
The sum of the numbers is the average times how many there are, and the first number is one part of that sum.
Sum of the four numbers \(=4\times40=160\)
Let the first number be \(x\); the other three add up to \(160-x\).
\(\displaystyle x=\frac{160-x}{3}\)
\(3x=160-x\), so \(4x=160\) and \(x=40\)
Shortcut: If the first number is one-third of the rest, the rest is 3 parts and the first is 1 part: 4 equal parts make 160, so the first number is \(160\div4=40\).