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Doctors Medicines MCQs Q&A

  1. 22.5 days
  2. 27.5 days
  3. 30 days
  4. 37.5 days
  5. 40 days
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1 Answers

Option 4 : 37.5 days

Given:

P can complete 1/5 of the work in 5 days

Q can complete 1/6 of the same work in 5 days

with the help of R they can complete half of the work in 5 days

Concept used:

If the work is constant, then

Time taken ∝ 1/ Efficiency.

Calculation:

Let the total work be 1

P takes 5 days to complete 1/5 work

Total work will be completed in 25 days

A work 1/25 in 1 day

Q takes 5 days to complete 1/6 work

Total work will be completed in 30 days

Q work 1/30 in 1 day

P and Q one day work = 1/25 + 1/30

⇒ P + Q = (6 + 5)/150

⇒ P + Q = 11/150

P and Q completed half of the work

⇒ (11/150) × 2 = 11/75

Half of the work is completed in 5 days by P, Q and R and efficiency is 1/5

⇒ P + Q + R - (P + Q) = (1/5) - (11/75)

⇒ Q = (15 - 11)/75 = 4/75

Q takes 75/4 days to complete the half of the work, total work will be completed in

⇒ (75/4) × 2

⇒ 150/4 = 37.5 days

∴ R will take 37.5 days to complete the same work.

Alternate Method

Formula used:

Work = Time × Efficiency

P complete whole work in 25 days

Q complete whole work in 30 days

 

Time

Total work (LCM of time)

Efficiency

P

25

 

6

 

 

150

 

Q

30

 

5

P, Q and R complete the half work in 5 days

Efficiency = 75/5 = 15

R efficiency is 15 - 11 = 4

Time taken by R to complete the total work alone is

⇒ 150/4 = 37.5 days

∴ R will take 37.5 days to complete the same work.

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