# 3 men P, Q, and R can complete a piece of work in 20, 24, and 30 days respectively. P, Q, and R start working together but, after 4 days, P leaves off

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3 men P, Q, and R can complete a piece of work in 20, 24, and 30 days respectively. P, Q, and R start working together but, after 4 days, P leaves off and after the next 4 days, R too leaves off. Then find how many days will the whole work take to be completed?
1. 15.7 days
2. 8.8 days
3. 12.8 days
4. 10 days

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Correct Answer - Option 3 : 12.8 days

Given:

P can do a piece of work = 20 days

Q can do a piece of work = 24 days

R can do a piece of work = 30 days

After the next 4 days, P left and after the next 4 days R also left

Concept used:

Total work = LCM

Formula used:

Efficiency = Work/Time

Calculations:

Total work = LCM = 120

 Person Time Total work Efficiency P 20 days 120 120/20 = 6 Q 24 days 120 120/24 = 5 R 30 days 120 120/30 = 4

Total efficiency of P, Q, and R = 15

In first 4 days’ work done by P, Q and R = 15 × 4 = 60

Remaining work = 120 – 60 = 60

Q + R efficiency = 5 + 4 = 9

P left and In next 4 days work done by Q and R = 9 × 4 = 36

Remaining work = 60 – 36 = 24

Now, R left and Time taken by Q to complete the remaining work = 24/5 = 4.8

Total time taken to complete the work = 4 + 4 + 4.8 = 12.8 days

Total time taken to complete the work is 12.8 days