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1. 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 ?

A. 850

B. 895

C. 955

D. 960

Solution:

Let the number be x
Then,

\begin{aligned} \frac{3}{5} of \frac{2}{3} of x - \frac{2}{5} of \frac{1}{4} of x = 288 \\ \Leftrightarrow (x \times \frac{3}{5} \times \frac{2}{3}) - (x \times \frac{2}{5} \times \frac{1}{4}) = 288 \\ \Leftrightarrow \frac{2}{5} x - \frac{1}{10} x = 288 \\ \Leftrightarrow \frac{3 x}{10} = 288 \\ \Leftrightarrow x = (\frac{288 \times 10}{3}) \\ \Leftrightarrow x = 960 \end{aligned}

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