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

Solution(By Examveda Team)

Let the number be x
Then,
$$\eqalign{ & \frac{3}{5}{\text{of }}\frac{2}{3}{\text{of }}x - \frac{2}{5}{\text{of }}\frac{1}{4}{\text{of }}x = 288 \cr & \Leftrightarrow \left( {x \times \frac{3}{5} \times \frac{2}{3}} \right) - \left( {x \times \frac{2}{5} \times \frac{1}{4}} \right) = 288 \cr & \Leftrightarrow \frac{2}{5}x - \frac{1}{{10}}x = 288 \cr & \Leftrightarrow \frac{{3x}}{{10}} = 288 \cr & \Leftrightarrow x = \left( {\frac{{288 \times 10}}{3}} \right) \cr & \Leftrightarrow x = 960 \cr} $$