50 daily workers can complete a dam project in 40 days. if 30 of them work daily and rest work in every alternative day. how many more day will be required?
Answers
30*40=1200
20*20=400
Total =1600
2000………. 1 work
1600…………1600/2000 work or 4/5 work
remain, 1- 4/5=1/5 work
1600….4/5…… 40 days
1600…..1……….(40*5)/4=50
1600…..1/5……..50/5 =10 days
Another Approach:
Total work= 50*40= 2000
In 40 days, daily workers complete: 30*40=1200
Alternate workers complete:20 * (40/2) = 400
Let us assume that they work for x days after 40 days.
Alternate workers will work for x/2 days.
A/Q, 2000 = 1200 + 400 + 30x + 20*(x/2)
Solving, we get x=10
Ans: 10 days
Acc to the question,
50 daily workers can complete a dam project in 40 days.
That means 1 worker will take (40 x 50) days to complete.
or, In 1 day 1 worker can finish = 1/2000 part of the work.
Now, as per the question on the first day 30 men will work and on the 2nd day 50 men works, again on 3rd day 30 men works and on 4th day 50 men and so on.
Amount of work done in 1 day by 30 men = 30/2000 = 3/200 part of the work.
Amount of work done in 1 day by 50 men = 50/2000 = 1/40 part of the work.
Since the pattern of 30 men, 50 men is consistent so we can form a pair of it to find the combined work done.
So, the amount of work done in every 2 days will be = (3/200 + 1/40) part of the work.
or, 8/200 = 1/25 part of the work.
Thus, in 2 days 1/25 part of the work is done.
So, the complete work will be done in 2 x 25 days = 50 days.
Therefore, if 30 of them work daily and rest work in every alternative day (50 - 40) = 10 more days will be required.