Question

Instead of multiplying a given number by $\frac{8}{19}$, a student divided it by $\frac{8}{19}$. His answer was $297$ more than the correct answer. The given number is

• A. $123$
• B. $152$
• C. $178$
• D. $197$

Answer 1

The correct option is B $152$

Let the given number be x.
Instead of multiplying, $\frac{x\times 8}{19}$, he divided, $\frac{x}{8/19}$
The correct answer would be $\frac{8x}{19}$.
His answer is $\frac{19x}{8}=\frac{8x}{19}+297$. Therefore,
$\frac{19x}{8}=\frac{8x+297\times 19}{19}$
or $361x=8(8x+297\times 19)=64x+297\times 19\times 8$
or $361-64x=297\times 19\times 8$
or $297x=297\times 19\times 8$
$\therefore x=19\times 8=152$