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 divided the given number by 4, which resulted in a value 5 short of the correct value. What is the initial number?
A300 ✓ Correct
B400
C350
D450
Correct answer: (A) 300
Explanation
The number is 300.
The correct result is N/(2 x 5) + N/(2 x 3) = N/10 + N/6 = 4N/15.
The student computed N/4, which was 5 less than the correct value.
So 4N/15 - N/4 = 5.
Common denominator: 16N/60 - 15N/60 = N/60 = 5.
N = 5 x 60 = 300.
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