Question

28 is divided into two parts in such a way that $\frac{6}{5}$ of one part is equal to $\frac{2}{3}$ of the other. What would be the smaller part?

• A. 8
• B. 9
• C. 10
• D. 18

Answer 1

The correct option is C

10

Let one part be $x$.

Then, other part = $28-x$

Given that
$\frac{6}{5}$ of one part = $\frac{2}{3}$ of the other
$\Rightarrow \frac{6}{5}x=\frac{2}{3}(28-x)$
$\Rightarrow \left(\frac{6\times 3}{2}\right)x=5(28-x)$
$\Rightarrow 9x=5(28-x)$
$\Rightarrow 9x=140-5x$
$\Rightarrow 14x=140$
$\Rightarrow x=10$

The other part would be 28 - 10 = 18
Hence, the smaller part is 10.