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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. $21:20$

2 Answers

Best answer
10 votes
10 votes

Correct answer is C.

Q can finish the task in $25$ days, working alone for $12$ hours a day.

What can we learn from this line??

That Q, in $25\times 12$ hours can complete the work alone.

That is, his rate of doing work per hour is $\frac{1}{25\times 12}=\frac{1}{300}.$

R can finish the task in $50$ days, working alone for $12$ hours per day.

Now, similarly, R's per hour work is $\frac{1}{600}.$

Now, Q has worked for $5$ days of $12$ hours ($60$ hours) and R for $7$ days of $18$ hours ($126$ hours).

We finally know, how many hours both worked, and their capacity for an hour.

Ratio of work done by Q and R after $7$ days from the start of the project

$\qquad\qquad=\frac{\text{Work done by Q}}{\text{Work done by R}} = \frac{60\times \frac{1}{300}}{126\times  \frac{1}{600}}=\frac{20}{21}.$

edited by
0 votes
0 votes

When both working 12 Hours a day


Q’s 1 day work→ x /25


R’s 1 day work→ x/50

After 7 Days 


Q could only work for 5 days as he took 2 days leave  hence = 5x/25..


R worked 18Hours per day in that week...18*7 = 126 = which is for him Working 10 days and 1 half day.


So 10x/50 + x/(50*2) = 21x/100

In short Q worked for 5x/25 in a week


R worked for 21x/100

Ratio is 20:21...C is the answer
 

Answer:

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