Q-13. Deepak starts a work and work for 12 days and find he has completed 10% less work which he
had to finish in order to complete the work in 24 days, so he ask Rahman to join him to finish the
work on time. If Rahman work half day only for the remaining days. Find the efficiency of Rahman
is what percent less than the efficiency of Deepak?
Answers
Rahman's efficiency is 400 % less than that of Deepak.
• Let the total work to be completed be 100.
• Deepak had to complete the entire work alone in 24 days.
=> Work to be done by Deepak in 24 days = 100
=> Work to be done by Deepak in 1 day = 100 / 24
• Given, Deepak works for 12 days.
=> Work that should have been completed by Deepak in 12 days = (100 / 24) × 12 = 50
But, Deepak finished 10 % work less than 50.
=> Work done by Deepak in 12 days = 50 - (10 % 100)
= 50 - (10 × 100) / 100
= 50 - 10
= 40
• Therefore, work still left to be done = 100 - 40 = 60
• Number of days remaining = 12
• Now, Rahman joins Deepak and they together complete the remaining work on time, means in the next 12 days.
• Work done by Deepak and Rahman together in 12 days = 60
=> Work done by both in 1 day = 60/12 = 5
• Let us consider that Rahman takes x days to complete the whole work alone.
=> In 1 day, Rahman completes 100/x work.
• Work done by Deepak and Rahman together in 1 day :
( 100/24 )+ ( 100/x ) = 5
=> 100x + 2400 = 5 × 24x
=> 100x + 2400 = 120x
=>20x = 2400
=> x = 120 days
Therefore, Rahman alone completes the work in 120 days.
• As we can see, Rahman alone completes the work in 120 days, whereas, Deepak takes only 24 days to complete the work alone.
• Therefore, Rahman is quite less efficienct than Deepak.
Percentage by which Rahman is less efficienct than Deepak = (Difference between their number of days / Deepak's number of days) × 100 %
= {120 - 24) / 24} × 100 %
= (96/24) × 100 %
= 400 %