Question

Two numbers are in the ratio $17:45$. One-third of the smaller number is less than $\frac{1}{5}$ of the bigger number by $15$. What is the smallest number?

• A. $25\frac{1}{2}$
• B. $67\frac{1}{2}$
• C. $76\frac{1}{2}$
• D. $86\frac{1}{2}$

Answer 1

Answer: (C)

$76\frac{1}{2}$

Let the numbers be $17x$ and $45x$.

Then $\frac{1}{3}$ of number 17x =$\frac{17x}{3}$

And $\frac{1}{5}$ of number 45x=$\frac{45x}{5}$

As per question one third of the smaller number is less then $\frac{1}{5}$ of the bigger number by $15$

$\therefore 17x\times \frac{1}{3}+15=\frac{1}{5}\times 45x$

$\Rightarrow 85x+225=135x$

$\Rightarrow 135x-85x=225$

$\Rightarrow 50x=225$

$\Rightarrow x=\frac{9}{2}$

Then smaller number=$17\frac{9}{2}=\frac{153}{2}=76\frac{1}{2}$