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GATE 2016 EC – Question 10

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?

  1. 10:11
  2. 11:10
  3. 20:21
  4. 21:20

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Correct answer: (C) 20:21

Explanation

Q needs $25 \times 12 = 300$ hours in total. Q worked for $7 - 2 = 5$ days at 12 hours, which is 60 hours, so Q did $\frac{60}{300} = \frac{1}{5}$ of the work. R needs $50 \times 12 = 600$ hours in total and worked $7 \times 18 = 126$ hours, so R did $\frac{126}{600} = \frac{21}{100}$. The ratio is $\frac{1/5}{21/100} = \frac{20}{21}$.