Instructions: The following pie chart shows the hourly distribution in a day (in degrees) of all the major activities of a student. A day has 24 hours. The pie chart shows: Games 30°, Home work 45°, School 105°, Sleeping 120°, Others 60° (total 360°).

If he spends the time in games equal to the home work, and the other activities remain constant, what is the percentage decrease in the time spent sleeping?

Question

The monthly salary for a person who follows the same expense pattern, but has a petrol expense of Rs 500 p.m., is:

Answer 1

This question is really about tracking where a 15° gain in one slice of the pie must come from, given that most of the pie is fixed.

Games needs to grow from $30°$ to $45°$ (matching home work), a gain of $15°$.
Home work, School, and Others are all explicitly held constant, so they cannot supply this extra $15°$.
Since the full circle stays at $360°$, the only remaining slice, Sleeping, must shrink by exactly $15°$ to balance the books.
Sleeping's percentage drop, relative to its own original size, is $\frac{15}{120} \times 100 = 12.5\%$.

So the correct answer is option B, 12.5%.

Answer 2

This question is really about tracking where a 15° gain in one slice of the pie must come from, given that most of the pie is fixed.

Games needs to grow from $30°$ to $45°$ (matching home work), a gain of $15°$.
Home work, School, and Others are all explicitly held constant, so they cannot supply this extra $15°$.
Since the full circle stays at $360°$, the only remaining slice, Sleeping, must shrink by exactly $15°$ to balance the books.
Sleeping's percentage drop, relative to its own original size, is $\frac{15}{120} \times 100 = 12.5\%$.

So the correct answer is option B, 12.5%.

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