The difference between $\frac{3}{4}$ th of $\frac{4}{5}$ th of a number and $\frac{1}{6}$ th of $\frac{2}{5}$ th of the same number is 648 . What is the number?
(a)1110
(b)1215
(c)1325
(d)1440
(e)None of these
Answer
Answer (as printed): B
Explanation
Let the number be $x$. Then, $$\begin{aligned} & \frac{3}{4} \text { of } \frac{4}{5} \text { of } x-\frac{1}{6} \text { of } \frac{2}{5} \text { of } x=648 \\ \Rightarrow \quad & \frac{3 x}{5}-\frac{x}{15}=648 \Rightarrow \frac{8 x}{15}=648 \Rightarrow x=\frac{648 \times 15}{8}=1215 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.