Sixty men can build a wall in 40 days, but though they begin the work together, 5 men quit every ten days. the time needed to build the wall is:
Answers
Given info : 60 men can build a wall in 40 days, but though they begin the work together, 5 men quit every ten days.
To find : the time needed to build the wall is...
solution : a/c to question, 60 men can build a wall in 40 days.
Total work = 60 × 40 = 2400 .
but here also given that, every 10 days 5 men quit.
So,
Total work = 2400
first 10 days ⇒ 60 × 10 = 600
2nd 10 days ⇒55 × 10 = 550
3rd 10 days ⇒50 × 10 = 500
4th 10 days ⇒45 × 10 = 450
if we add it we get, 600 + 550 + 500 + 450 = 2100
So, rest 300 work done by 40 men in 300/40 = 7.5 days
Therefore total days need to build the wall = 10 + 10 + 10 + 10 + 7.5 = 47.5 days
"60 men can build a wall in 40 days
"Fraction of work done by 1 men in 1 day =1/(60*40) = 1/2400
"In 1st 10 days fraction of work done = 1/2400*10*60 = 1/4 =12/48
"Next 10 days fraction of work done
= 1/2400*10*55 = 11/48
"Next 10 days fraction of work done
= 1/2400*10*50 = 5/24 =10/48
"Next 10 days fraction of work done
= 1/2400*10*45 = 3/16 =9/48
"In 40 days fraction of work done
= (12+11+10+9)/48 = 42/48
"Remaining fraction of work = 6/48 = 1/8
"if x is the no of days to complete 1/8 work with 40 men, then
"1/2400*x*40 = 1/8
"x = 15/2
"total no of days required = 10+10+10+10+15/2 = 47 1/2days
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