P does 3/4 of a piece of work in 15 days, and with the assistance of Q

P does 3/4 of a piece of work in 15 days, and with the assistance of Q, they finish the remaining work in 3 days. How long Q alone will take to whole work? 1. 15 days2. 20 days3. 25 days4. 30 days

Answer» Correct Answer - Option 4 : 30 days

Given:

P does 3/4 of a piece of work = 15 days

When Q comes then both fished the work = 3 days

Concept used:

Total work = LCM

Formula used:

Efficiency = Work/Time

Calculations:

P does 3/4 of a piece of work = 15 days

Time taken by P to complete the total work = 15 × 4/3 = 20 days

Remaining work = 1 – 3/4 = 1/4

So, P + Q work 1/4 in 3 days

Now, Time taken by P and Q to complete the work total work together = 3 × 4/1 = 12 days

Total work = LCM = 60

Person	Time	Total work	Efficiency
P	20 days	60	60/20 = 3
P + Q	12 days	60	60/12 = 5

Efficiency of Q = 5 – 3 = 2

Time taken by Q to complete the work alone = 60/2 = 30 days

∴ Time taken by Q to complete the work alone is 30 days

Discussion

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