A student was asked to divide half of a number by 5 and the other half by 3 and then add the two quantities. Instead of doing all this the student divides the given number by 4 which results into 5 short of the correct value. What is the initial number?

Calculation:

Let's assume the initial number as x.

According to the given information, the student was supposed to divide half of the number by 5 and the other half by 3, and then add the two quantities.

Half of the number divided by 5: (x/2) / 5 = x/10

The other half of the number divided by 3: (x/2) / 3 = x/6

The student, however, divides the given number by 4, resulting in 5 less than the correct value:

⇒ (x/4) = (x/10) + (x/6) - 5

To simplify the equation, we'll find a common denominator:

⇒ (x/4) = (3x/30) + (5x/30) - 5

⇒ (x/4) = (8x/30) - 5

Multiplying both sides of the equation by 60 to eliminate the fractions:

⇒ 15x = 16x - 300

⇒ x = 300

Therefore, the initial number is 300.

So the answer is:300