Question

The average of three numbers is $60$. The first is $\frac{1}{4}$th of the sum of the other two. The first number is:

• A. $24$
• B. $36$
• C. $48$
• D. $72$

Answer 1

The correct option is B $36$

Given, the average of three numbers is $60$.

Let the three numbers be $a_1,a_2,a_3$.

Therefore, average = $\frac{a_1+a_2+a_3}{3}$

$⟹\frac{a_1+a_2+a_3}{3}=60$

$⟹a_1+a_2+a_3=60\times 3=180$ ———(1).

Given that first term is $(\frac{1}{4}{)}^{th}$ of the sum of the other two.

$⟹a_1=\frac{1}{4}(a_2+a_3)$

$⟹a_2+a_3=4a_1$ ——-(2).

Substituting (2) in (1), we get,

$⟹a_1+4a_1=180$

$⟹5a_1=180⟹a_1=\frac{180}{5}=36$.

Therefore, the first number is $36$.

Hence, option $36$ is correct.