Question

A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?
A. 10%
B. 15%
C. 20%
D. 25%
E. 30%

Answer 1

Hint: We first try to find the starting speed of work for grading 5 papers in 30 minutes. We then find the remaining time and work. We find the new speed of work for grade the remaining papers in the allotted time and also find its increase in percentage.

Complete step-by-step answer:
A teacher has 3 hours to grade all the papers submitted by the 35 students in her class.
3 hours is equal to $ 3\times 60=180 $ minutes.
She gets through the first 5 papers in 30 minutes. Therefore, the teacher evaluates at the speed of $ 5\times 2=10 $ papers per hour as 1 hour is equal to 60 minutes.
The remaining time is $ 180-30=150 $ minutes.
The number of papers remaining is $ 35-5=30 $ .
The teacher has to evaluate 30 papers in 150 minutes to grade the remaining papers in the allotted time.
We try to find the number of papers she has to grade in 1 hour which is equal to 60 minutes.
So, she has to evaluate 30 papers in 150 minutes. This means she evaluates $ \dfrac{30}{150}=\dfrac{1}{5} $ papers in 1 minutes. She has to evaluate $ \dfrac{1}{5}\times 60=12 $ papers in 1 minutes.
The increase in number is $ 12-10=2 $ papers in 1 hour.
The percentage increase is $ \dfrac{2}{10}\times 100=20 $ .
She has to work 20% faster to grade the remaining papers in the allotted time.
The correct option is C.
So, the correct answer is “Option C”.

Note: We need to remember in case of finding comparison the time has to be the same for both measurements. That’s why we took the time mark as 1 hour for both speeds of work.