Aman verma wrote:Q: Two friends undertake to do a job. The second friend started working 2 hours after the first. Five hours after the second friend has begun working, there is still 9/20 of the work to be done. When the assignment is completed, it turns out that first friend has done 60% of the work, while second friend has done the rest of the work. How many hours would it take each one to do the whole job individually ?
a) 10 hours and 12 hours
b) 15 hours and 10 hours
c) 20 hours and 25 hours
d) 18 hours and 20 hours
e) 16 hours and 22 hours
ps: This problem can be very easily solved by plugging in the options but can this be solved algeraically ?
I would plug in the answers, which represent the time for each friend to complete the job alone.
Answer choice C: 20 hours and 25 hours.
Let work = 100 units.
Rate for the first friend = w/t = 100/20 = 5 units per hour.
Rate for the second friend = w/t = 100/25 = 4 units per hour.
Work completed by the first friend in 2 hours = r*t = 5*2 = 10 units.
Combined rate for the two friends = 5+4 = 9 units per hour.
Rate completed by the two friends in the next 5 hours = r*t = 9*5 = 45 units.
Remaining work = 100-10-45 = 45 units.
Remaining work/Total work = 45/100 = 9/20.
Success!
No need to do more work.
Each answer choice offers a different ratio of times.
If we plug in any other time ratio, there will not be 9/20 of the work left to be completed after the initial 7 hours.
The correct answer is
C.
For the skeptical:
Time for the two friends to complete the remaining work = w/r = 45/9 = 5 hours.
Total time worked by the first friend = 12 hours.
Work produced by the first friend in 12 hours = r*t = 12*5 = 60 units.
(Work produced by the first friend)/Total work = 60/100 = 60%.
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