Question

The difference between ${\left(\frac{3}{5}\right)}^{th}$of ${\left(\frac{2}{3}\right)}^{rd}$ of a number and ${\left(\frac{2}{5}\right)}^{th}$ of ${\left(\frac{1}{4}\right)}^{th}$ of the same number is $288$. What is the number?

• A. $960$
• B. $850$
• C. $895$
• D. $995$

Answer 1

The correct option is A $960$

$\Rightarrow$ Let the number be $x$.

According to the given condition,

$\frac{3}{5}\times \frac{2}{3}\times x-\frac{2}{5}\times \frac{1}{4}\times x=288$

$\Rightarrow$ $\frac{2}{5}x-\frac{2}{20}x=288$

$\Rightarrow$ $\frac{8x-2x}{20}=288$

$\Rightarrow$ $6x=5760$

$\therefore$ $x=\frac{5760}{6}=960$

$\therefore$ The required number is $960.$