Question

What is the value of $x$ when $5\frac{1}{2}:x::8\frac{1}{2}:\frac{1}{4}$?

• A. $\frac{11}{69}$
• B. $\frac{11}{68}$
• C. $\frac{12}{68}$
• D. $\frac{11}{78}$

Answer 1

The correct option is B

$\frac{11}{68}$

$5\frac{1}{2}=\frac{11}{2}$

$8\frac{1}{2}=\frac{17}{2}$

So, $5\frac{1}{2}:x::8\frac{1}{2}:\frac{1}{4}$

= $\frac{11}{2}:x::\frac{17}{2}:\frac{1}{4}$

In a proportion, Product of means = product of extremes

$\Rightarrow x\times \frac{17}{2}=\frac{11}{2}\times \frac{1}{4}$

$\Rightarrow \frac{17x}{2}=\frac{11}{8}$

$\Rightarrow 17x=\frac{11}{8}\times 2$

$\Rightarrow x=\frac{11}{68}$