N workers can finish a job in 15 days. After working 5 days

Question

N workers can finish a job in 15 days. After working 5 days, additional 8 workers joined them. Together, they finished remaining job in 6 days. What is the value of n?

A. 15
B. 18
C. 24
D. 12
E. 9

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Aryaa03 · Answer

Sol:  IMO-Option-D

R = Rate per worker ;
n = no. of worker
Total number of work units = 1

1) (R.n)* 15 = 1 ==> R = 1/15n
2) If n no. of workers worked for 5 days instead of 15 , 1/3 of the total work completed would be completed
     Mathematically, (R.n)*5 = x , where R = 1/15n ==> x = 1/3
3) Remaining work = 1- x = 1-1/3 = 2/3 and no. of workers = (n+8) finish the remaining work in 6 dys
    R(n+8)*6 =  2/3
    Subsitute R = 1/15n and solve for n ==>  n= 12

Shubhradeep · Answer

Correct option should be D

let's take it this way:
each worker does 1 unit work each day. So, in 15 days n workers will be able to do 15n units work.
So, let's suppose total eork is 15n units

Now, the n workers work for first 5 days in which they complete 5n units work. Then 8 more workers join them.
So, total workers now = (n+8) who work for 6 more days to complete 15n units of work.

Hence, we can write -> 15n = 5n + 6(n+8)
 => 4n=48 => n=12

Correct option is D

PranavVyas · Answer

N*15units
5 days working, N workers have done N*5 units of work, and the remaining work is 
N*15-N*5 = N*10 units
(N+8)*16 units
N*10=(N+8)*6
4n=48
N=12

IMO-D

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unraveled · Answer

N workers can finish a job in 15 days. After working 5 days, additional 8 workers joined them. Together, they finished remaining job in 6 days. What is the value of n?

A. 15
B. 18
C. 24
D. 12
E. 9

We know that it takes 15 days to complete the work. Now that 5 days work is done we now have  \frac{1}{3}  work done since  \frac{5}{15}  and left with  1 - \frac{1}{3} = \frac{2}{3}  work to be done by N + 8 workers in 6 days.
Now, the fraction of number of persons who worked initially(N) and numbers of persons who worked later(N+8) would be equal to the ratio of work left to be done and work done in 6 days(6 units). Here the assumption is that rate of work done by individual is same foe each worker.
Thus,
 \frac{N}{N+8} = \frac{6}{10} 
10N = 6N + 48
N = 12

Answer D.

N workers can finish a job in 15 days. After working 5 days

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GMAT Problem Solving (PS) Questions

N workers can finish a job in 15 days. After working 5 days

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