Question
A company has to construct a flyover. It deployed 10 men who can finish the work 30 days each working 8 hrs a day. After five days of work due to heavy rain 50% of the flyover constructed so far collapsed. After the incident the management decided to stop the construction work during the period it rains. Also the Management deployed 5 more men and 10 women to complete the project faster. From the sixth day onwards it rained every alternative day for 2 hours each. Find the fraction of construction work left after the 17th day. Assume that all the men work with same efficiency, and all women workwith half of the efficiency of men. Also assume that it rains only during the working hours.
Answer: Option D
:
D
Work completed in 5 days = (16). Since 50% of the bridge collapsed so total work completed after 5 days =
(112) Remaining work after 5 days = (1112)
Since women efficiency is half so 10 women will finish the work in 60 days i.e each day they will finish (160)part of work.
15 men will finish = (120)part of work every day. So from the sixth day onwards the work finished everyday =120+160=115.Now from sixth days onwards it rains alternatively for 2 working hours.
Hence total numbers of hours lost = 6×2 = 12 hrs = 1.5 days ( 8 hrs per day)
So till 17th day instead of remaining 12 days the work was done effectively on only 10.5 days.
So the work completed in 10.5 days =1015+130=2130.
Fraction of work left after 17th day = work left after 5 days - work done in 12 days =1112−2130=1360
Hence option D is correct.
Alternative approach: (using units of work done)
Total number of units of work to be done = 10×30×8 = 2400
In the first 5 days, 10×5×8 =400 units of word is done. However, 200 units of work is lost
Thus, remaining work is 200 units
From the 6thday 5 more men and 10 more women are joining in ⇒ 10 more men are joining in
Thus, on every day that it rains; number of units of work done =6×20=120
And on every day that it does not rain; number of units of work done =8×20=160
Total units of work done =120×6+160×6+200=1880
Remaining work = 2400-1880 = 540. Required ratio =(5402400)=(1360)
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:
D
Work completed in 5 days = (16). Since 50% of the bridge collapsed so total work completed after 5 days =
(112) Remaining work after 5 days = (1112)
Since women efficiency is half so 10 women will finish the work in 60 days i.e each day they will finish (160)part of work.
15 men will finish = (120)part of work every day. So from the sixth day onwards the work finished everyday =120+160=115.Now from sixth days onwards it rains alternatively for 2 working hours.
Hence total numbers of hours lost = 6×2 = 12 hrs = 1.5 days ( 8 hrs per day)
So till 17th day instead of remaining 12 days the work was done effectively on only 10.5 days.
So the work completed in 10.5 days =1015+130=2130.
Fraction of work left after 17th day = work left after 5 days - work done in 12 days =1112−2130=1360
Hence option D is correct.
Alternative approach: (using units of work done)
Total number of units of work to be done = 10×30×8 = 2400
In the first 5 days, 10×5×8 =400 units of word is done. However, 200 units of work is lost
Thus, remaining work is 200 units
From the 6thday 5 more men and 10 more women are joining in ⇒ 10 more men are joining in
Thus, on every day that it rains; number of units of work done =6×20=120
And on every day that it does not rain; number of units of work done =8×20=160
Total units of work done =120×6+160×6+200=1880
Remaining work = 2400-1880 = 540. Required ratio =(5402400)=(1360)
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