Question

M can do a piece of work in 20 days. He works at it alone for 5 days and N alone finishes the remaining work in 9 days. In how many days, both of them together can complete the work ?
1. 12.5 days
2. 8 days 
3. 10 days 
4. 7.5 days 

Answer 1

Correct Answer - Option 4 : 7.5 days 

Given:

M finishes a task in 20 days

M works for 5 days alone and N does the remaining work in 9 days alone.

Calculation:

M finishes the work in 20 days

So, work done by M in 1 day = 1/20 

Work done by M in 5 days =  1/20 × 4 = 1/5

Remaining work = 1 - (1/5)  = 4/5

So, 4/5 work is done by N in 9 days.

If the whole work is done by n,

9 × (5/4) = 45/4

So, work done by N in 1 day = 4/45

(A + B)'s one day of work = (1/ 20) + (4/45) 

= 125/900

∴ M and N will both finish work in 900 / 125 days ~ 7.5 days