Question

The highest score of a certain data exceeds in lowest score by $16$ and coefficient of range is $\frac{1}{3}$. The sum of the highest score and the lowest score is

• A. $36$
• B. $48$
• C. $24$
• D. $18$

Answer 1

The correct option is B $48$

Let the highest score be $x_m$ and

the lowest score be $x_0$

Given that highest score exceeds lowest score by $16$

$⟹x_m=x_0+16⟹x_m-x_0=16$ ————(1)

Coefficient of range is given by $\frac{x_m-x_0}{x_m+x_0}$

Given that coefficient of range is $\frac{1}{3}$

$⟹\frac{x_m-x_0}{x_m+x_0}=\frac{1}{3}$ ———(2)

Substitute (1) in (2) we get

$\frac{16}{x_m+x_0}=\frac{1}{3}$

$⟹x_m+x_0=16\times 3=48$

Therefore sum of the highest score and lowest score is $48$