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1. A student was asked to divide the half of a certain number by 6 and the other half by 4 and then to add the two quantities so obtained. Instead of doing so the student divided the number by 5 and the result fell short by 4. The given number was ?

A. 240

B. 288

C. 384

D. 480

Solution:

Let the number be x
Then,

\begin{aligned} \Leftrightarrow [\frac{(\frac{x}{2})}{6} + \frac{(\frac{x}{2})}{4}] - \frac{x}{5} = 4 \\ \Leftrightarrow \frac{x}{12} + \frac{x}{8} - \frac{x}{5} = 4 \\ \Leftrightarrow \frac{10 x + 15 x - 24 x}{120} = 4 \\ \Leftrightarrow x = 4 \times 120 \\ \Leftrightarrow x = 480 \end{aligned}

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