Question

Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 44. Find the largest number.

• A. $38$
• B. $48$
• C. $62$
• D. $72$

Answer 1

The correct option is D $72$

Let the three numbers be $x_1,x_2,x_3$

Given that second is twice the first.

$⟹x_2=2x_1$

$⟹x_1=\frac{1}{2}{x}_2$ --------(1)

Given that second is thrice the third.

$⟹x_2=3x_3$

$⟹x_3=\frac{1}{3}{x}_2$ --------(2)

Given that average of three numbers is $44$

$⟹44=\frac{x_1+x_2+x_3}{3}$

$⟹x_1+x_2+x_3=44\times 3=132$ -------(3)

substituting (1) and (2) in (3) we get

$\frac{1}{2}{x}_2+x_2+\frac{1}{3}{x}_2=132$

$⟹\frac{x_2}{6}(3+6+2)=132$

$⟹11x_2=132\times 6$

$⟹x_2=\frac{132\times 6}{11}$

$⟹x_2=72$

$⟹x_1=\frac{1}{2}{x}_2=\frac{72}{2}=36$

$⟹x_3=\frac{1}{3}{x}_2=\frac{72}{3}=24$

Therefore the largest number is $x_2=72$