Question

P can do work in 20 days and Q can do the same in 40 days. If they start the work together and P leaves that work 10 days before completion. In how many days the work will be finished?
1. 15 days
2. 20 days
3. 30 days
4. 10 days

Answer 1

Correct Answer - Option 2 : 20 days

Given:

P can do a piece of work = 20 days

Q can do a piece of work = 40 days

P leaves that work 10 days before completion

Concept used:

Total work = LCM

Formula used:

Efficiency = Work/Time

Calculations:

Total work = LCM = 40

Person	Time	Total work	Efficiency
P	20 days	40	40/20 = 2
Q	40 days	40	40/40 = 1

 

Let the work finishes in x days

So, Time in which P works = (x – 10)

Work done by P in (x – 10) days = 2 × (x – 10)

Work done by Q in x days = 1 × x = x

Now,

⇒ 2(x – 10) + x = 40

⇒ 2x – 20 + x = 40

⇒ 3x = 60

⇒ x = 20 days

∴ Time in which the total work has completed is 20 days