Question

P, Q, R and S are working on a project. Q can finish the task in 25 days, working along 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?

• A.
  10 : 11
• B.
  11 : 10
• C.
  20 : 21
• D.
  21 : 20

Answer 1

The correct option is C

20 : 21
$Qcandoworkin25\times 12=300hrs$

$Rcandoworkin50\times 12=600hrs$

So we can say Q is twice efficient as R

Now Q worked only for 5 days @ 12 hrs/day.

$Sohewilldo60unitsofhiswork(TotalworkforQi.e300hrs)$

$hewilldoonly\frac{1}{5}ofwork$

$(\frac{60}{300}=\frac{1}{5})$

While R worked for all 7 days @ 18 hrs/day

So he will do 18$\times$7 = 126 of his work (Total work for 600hrs)

$Hewilldo\left(\frac{126}{600}\right)=\left(0.21\right)ofhiswork$

$Sorequiredratio\frac{1}{5}:\frac{126}{600}$

$120:126$

$20:21$