10 Men begin to work together on a job, but after some days, 4 of them left the job. As a result the job which could have been completed in 40 days is completed in 50 days. How many days after the commencement of the work did the 4 men leave?
A. 10
B. 15
C. 25
D. 30
Solution(By Examveda Team)
10 men complete the work in 40 days.
So, 1 man complete the same work = 10 *40 = 400 men-days.
Work rate of one man = 1/400
Let N = Number of days after start, 4 men leaves.
50 - N = Number of days after 4 men leave.
Now,
Work rate of one men * total men * number of days = Work completed
(1/400) * 10 * N = Part of job completed --------------------------- (1)
(1/400) * 6 * (50 -N) =Other Part of job completed --------------------------- (2)
Adding (1 ) and (2) get 1 work completed.
(1/400) * 10 * N + (1/400) * 6 * (50 -N) = 1
(1/400) [ 10N - 6N + 300] = 1
4N + 300 = 400
4N = 400 - 300
4N = 100
N = 100/4 = 25 days.
Thus, after 25 days 4 men left the work.
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If one man can do 1 work in one day, then 10 man do 10 work in 1 day.
Similarly
If 10 man do 10 work in in 1 day then, in 40 days they complete 10*40=400 work----1st
But the same work was completed in 50 days
According to first situations
If take to complete in 50 days by working 10 man then the whole work done by them is
10*50=500 work----2nd
But it happened only for 4 man leave the work after some days.
If we subtract the 1st work 400, from the 2nd work 500 then we get 100 work
500-400=100
It means before leaving that 4 man they do only 100 work
According to 1st situation
4 man do 4 work in 1 day then they take 25 day to complete the 100 work
100/4=25 days
It means that 4 person leaves the work after 25 days
Simply 500-400=100/4=25days
Actual work=Man*Time=10*40=400 units
ATQ,
400= 10*n+6(50-n)
Or, n=25 [ Ans.]
Please provide a short cut way fr this qstn
After 25 days