Question

Two numbers are in the ratio $17:45$. One third of the smaller is less than $\frac{1}{5}$ of the bigger by 15. The smaller no is

• A. $25\frac{12}{2}$
• B. $67\frac{12}{2}$
• C. $76\frac{1}{2}$
• D. $86\frac{1}{2}$

Answer 1

The correct option is C $76\frac{1}{2}$

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

Then, $\frac{1}{5}\times 45x-\frac{1}{3}\times 17x=15\Rightarrow 9x-\frac{17x}{3}=15$

$\Rightarrow \frac{27x-17x}{3}=15\Rightarrow \frac{10x}{3}=15$

$\Rightarrow 10x=15\times 3\Rightarrow x=\frac{45}{10}=\frac{9}{2}$

$\therefore$ Smaller number $=17\times \frac{9}{2}=76\frac{1}{2}$.