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 The given number was

The correct answer is (b) 288.

Let $x$ be the given number. The student was asked to divide the half of $x$ by 6 and the other half by 4, and then to add the two quantities so obtained. This gives:

$$\frac{x}{2} \div 6 + \frac{x}{2} \div 4 = \frac{x}{4} + \frac{x}{8} = \frac{3x}{8}.$$

Instead, the student divided the number by 5, which gives:

$$x \div 5 = \frac{x}{5}.$$

The result fell short by $\frac{3x}{8} – \frac{x}{5} = \frac{x}{40}$. Therefore, the given number is a multiple of 40. The only multiple of 40 among the given options is 288.