Question

$\frac{3}{4}$ is subtracted from a certain number which is then multiplied by $8$. The product is equal to the number multiplied by $\frac{2}{5}$. The number is

• A. $\frac{10}{13}$
• B. $\frac{15}{19}$
• C. $-\frac{3}{4}$
• D. $-1$

Answer 1

Answer: (B)

$\frac{15}{19}$

Let the number be $x$

The number subtracted by $\frac{3}{4}$ $=x-\frac{3}{4}$.......(1)

The number (1) multiplied by $8$ then the number is $8(x-\frac{3}{4})$ ............(2)

The number multiplied by $\frac{2}{5}$ is $\frac{2}{5}x$...........(3)

Given that number (2) and (3) are equal

$\therefore 8(x-\frac{3}{4})=\frac{2x}{5}$

Multiply by 8 both sides we get

$\frac{8(x-\frac{3}{4})}{8}=\frac{2x}{5\times 8}$

$\Rightarrow x-\frac{3}{4}=\frac{2x}{40}$

$\Rightarrow 40x-30=2x$

$\Rightarrow 40x-2x=30$

$\Rightarrow 38x=30$

$\Rightarrow x=\frac{30}{38}=\frac{15}{19}$