If M and N together can complete a piece of work in 4 days and N takes

If M and N together can complete a piece of work in 4 days and N takes twice as much days taken by M to complete the work alone, in how many days does M alone complete the whole work? 1. 6 days2. 4 days3. 10 days4. 12 days

Answer» Correct Answer - Option 1 : 6 days

Given:

M and N together can do a piece of work = 4 days.

N takes twice as much days alone as taken by M to complete the same piece of work.

Concepts used:

Total work = LCM

Efficiency = Work/Time

Calculation:

Let the number of days taken by M to complete the piece of work alone be 'a' days.

So, time taken by N alone to complete the work = 2a days

Total work = LCM of 'a' and '2a' = 2a

Person	Time	Total work	Efficiency
M	a	2a	2
N	2a	2a	1
M + N	4	2a	2 + 1 = 3

Time = Total work/Efficiency

⇒ 4 = 2a/3

⇒ a = 12/2 days

⇒ a = 6 days

Time taken by M to complete the work alone = a days = 6 days.

∴ M takes 6 days alone to complete a piece of work.

Discussion

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