A, B and C can finish a piece of work in 30, 40, and 60 days respectively. 10 days after they started to work together B leaves. 4 days after B left, A leaves and C completes the remaining work. Find how many days C had worked altogether.
This is how i did it: Please let me know if there is another easier way of solving it:
rate of A = 1/30
rate of B = 1/40
rate of C = 1/60
Work completed by all 3 in 10 days is W = rate * time
(1/30 + 1/40 + 1/60) * 10 = 3/4
Work left to complete = 1-3/4 = 1/4
Since B left after 10 days, the remaining work will have to be finished by A + C
rate of A + C together = (1/30 + 1/60)
Work done by A+C = (1/30 + 1/60) * 4 = 1/5
Work Left for C to complete alone = 1/4 - 1/5 = 1/20
Time required for C to complete 1/20 work alone = rate of C * time = 1/60 * time
Therefore time required for C to complete the remaining , 1/20 of the work @ 1/60 = 3 days
Total days worked by C = 10 + 4 + 3 = 17 days
Work problem
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1/30 + 1/40 + 1/60 = Completion in 1 day when working all 3 together = 8/240 + 6/240 + 4/240 = 18/240 = 9/120 = 3/40.
They all work together for 10 days - 3/40 * 10 = 30/40 = 3/4 done before B leaves.
B leaves - now working at 1/30(2/60) + 1/60 = 3/60 = 1/20 per day.
Do that for 4 days so 4*(1/20) = 1/5 completed before A leaves.
3/4 + 1/5 = 19/20 completed. All that's left is C now, working 1/60 per day. Needs to complete 1/20 or 3/60 units, so add 3 more days.
I'm getting a total of 10 days + 4 days + 3 days = 17 days.
They all work together for 10 days - 3/40 * 10 = 30/40 = 3/4 done before B leaves.
B leaves - now working at 1/30(2/60) + 1/60 = 3/60 = 1/20 per day.
Do that for 4 days so 4*(1/20) = 1/5 completed before A leaves.
3/4 + 1/5 = 19/20 completed. All that's left is C now, working 1/60 per day. Needs to complete 1/20 or 3/60 units, so add 3 more days.
I'm getting a total of 10 days + 4 days + 3 days = 17 days.
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Let job = 120 units.nadib002 wrote:A, B and C can finish a piece of work in 30, 40, and 60 days respectively. 10 days after they started to work together B leaves. 4 days after B left, A leaves and C completes the remaining work. Find how many days C had worked altogether.
Rate for A = w/t = 120/30 = 4 units per day.
Rate for B = w/t = 120/40 = 3 units per day.
Rate for C = w/t = 120/60 = 2 units per day.
Combined rate for A+B+C = 4+3+2 = 9 units per day.
Over 10 days, work completed by A+B+C = r*t = 9*10 = 90 units.
Combined rate for A+C = 4+2 = 6 units per day.
Over 4 days, work completed by A+C = 6*4 = 24 units.
Remaining work = 120-90-24 = 6 units.
Time for C to finish = w/r = 6/2 = 3 days.
Total days for C = 10+4+3 = 17 days.
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The approaches are the same: each determines respective rates for A, B and C.nadib002 wrote:Thank you all for replying
The answer is 17 days.
@Mitch
I saw that you plugged in numbers. I did it using algebra. When should one plug in numbers vs algebra?
Thank you
The key difference: by plugging in a value for the job, we can solve using only integer values. No messy fractions.
For most rate problems, I plug in a value for the job.
Use whichever approach you prefer.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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