Question

The average of four numbers is 48. If the first number is one-third of the sum of the remaining numbers, then the first number is:

• A. 36
• B. 54
• C. 48
• D. 60

Hint:

Express other numbers in terms of the first number and use the average formula to solve.

Answer 1

The Correct Option is A

Let the four numbers be \(x\), \(a\), \(b\), and \(c\), where \(x\) is the first number.
Average \(= \frac{x + a + b + c}{4} = 48 \Rightarrow x + a + b + c = 192\).
Given, \(x = \frac{1}{3}(a + b + c)\).
Substitute in the sum: \[ x + a + b + c = 192 \] \[ x + 3x = 192 \quad \Rightarrow \quad 4x = 192 \quad \Rightarrow \quad x = 48 \] Wait, the calculation suggests \(x=48\), but the options and the condition require careful check. Since \(x = \frac{1}{3} (a + b + c)\), then \(a + b + c = 3x\).
Sum of all four numbers: \[ x + (a + b + c) = x + 3x = 4x = 192 \Rightarrow x = \frac{192}{4} = 48 \] Hence, the first number is 48.