A, B and C working alone can complete a work in 24, 32, and 48 days respectively. "A" started the work and "B" joined him after 4 days and "C" joined them after 4 more days. If they were paid $10,800 for the work done, how much did "A" get ?
(A) 2800
(B) 3600
(C) 5400
(D) 6400
(E) 7600
OA is D
Thanks & Regards
Vinni
A, B and C working alone can complete a work in 24
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In 4 days, A completes 4/24 part of the whole work. Remaining work is 20/24 after 4 days.
When B joins after 4 days, A and B together do (1/24 + 1/32)*4 = 7/24. So remaining work after 8 days is (20/24 -7/24) =13/24.
When C joins after another 4 days, A, B and C can do (1/24 + 1/32+ 1/48) = 3/32 in 1 day. So, they need (32/3 * 13/24) = 52/9 days to complete the task.
This means, A works for a total of (4+4+52/9) days and in this he completes (4+4+52/9)*(1/24)=31/54 part of the whole task. So, A gets 10,800 * (31/54) = 6200.
I think choice D should be 6200.
When B joins after 4 days, A and B together do (1/24 + 1/32)*4 = 7/24. So remaining work after 8 days is (20/24 -7/24) =13/24.
When C joins after another 4 days, A, B and C can do (1/24 + 1/32+ 1/48) = 3/32 in 1 day. So, they need (32/3 * 13/24) = 52/9 days to complete the task.
This means, A works for a total of (4+4+52/9) days and in this he completes (4+4+52/9)*(1/24)=31/54 part of the whole task. So, A gets 10,800 * (31/54) = 6200.
I think choice D should be 6200.
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Another approach is to assign the entire job a certain number of units.vinni.k wrote:A, B and C working alone can complete a work in 24, 32, and 48 days respectively. "A" started the work and "B" joined him after 4 days and "C" joined them after 4 more days. If they were paid $10,800 for the work done, how much did "A" get ?
(A) 2800
(B) 3600
(C) 5400
(D) 6400
(E) 7600
Since the least common multiple of 24, 32 and 48 is 96, let's say that the entire job consists of 96 work units.
So, if A can complete the entire job (i.e., 96 work units) in 24 days, then A's rate is 4 units/day
Likewise, if B can complete the entire job (i.e., 96 work units) in 32 days, then B's rate is 3 units/day
And if C can complete the entire job in 48 days, then C's rate is 2 units/day
A works alone for 4 days. So, during this time, A completes 16 units of work.
This leaves us with 80 work units remaining (96 - 16 = 80)
A & B work together for 4 days. Their combined rate is 7 units/day (4+3=7). So, during this time, A+B complete 28 units of work.
This leaves us with 52 work units remaining (80 - 28 = 52)
A, B & C work together to complete job. Their combined rate is 9 units/day (4+3+2=9).
Since there are 52 work units remaining in the job, the number of days to complete the job = 52/9
IMPORTANT: 52/9 is not a nice number. However, since the answer choices are somewhat spread apart, I'm going to be somewhat aggressive with my estimation/rounding.
So, let's say that 52/9 = 6 (close enough).
This means that it takes A,B and C about 6 days to complete the rest of the job.
So, in total, A worked for approximately 14 days (4+4+6=14)
Since A works at a rate of 4 units/day, A completed a total of 56 work units (since 14x4=56).
The ENTIRE job was 96 work units. So, A did 56/96 of the work.
This means that A should get 56/96 of the $10,800 payment.
(56/96)(10,800) = (7/12)(10,800)
= $6300
Of course, none of the answer choices match $6300, but that's because we did some estimating/rounding earlier.
The closest answer choice is $6400, so the correct answer must be D
Cheers,
Brent
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Thanks Brent. Your solution is crystal clear, and i also believe that the word "approx" must be mentioned here.
Vinni
Vinni
Brent@GMATPrepNow wrote:
Another approach is to assign the entire job a certain number of units.
Since the least common multiple of 24, 32 and 48 is 96, let's say that the entire job consists of 96 work units.
So, if A can complete the entire job (i.e., 96 work units) in 24 days, then A's rate is 4 units/day
Likewise, if B can complete the entire job (i.e., 96 work units) in 32 days, then B's rate is 3 units/day
And if C can complete the entire job in 48 days, then C's rate is 2 units/day
A works alone for 4 days. So, during this time, A completes 16 units of work.
This leaves us with 80 work units remaining (96 - 16 = 80)
A & B work together for 4 days. Their combined rate is 7 units/day (4+3=7). So, during this time, A+B complete 28 units of work.
This leaves us with 52 work units remaining (80 - 28 = 52)
A, B & C work together to complete job. Their combined rate is 9 units/day (4+3+2=9).
Since there are 52 work units remaining in the job, the number of days to complete the job = 52/9
IMPORTANT: 52/9 is not a nice number. However, since the answer choices are somewhat spread apart, I'm going to be somewhat aggressive with my estimation/rounding.
So, let's say that 52/9 = 6 (close enough).
This means that it takes A,B and C about 6 days to complete the rest of the job.
So, in total, A worked for approximately 14 days (4+4+6=14)
Since A works at a rate of 4 units/day, A completed a total of 56 work units (since 14x4=56).
The ENTIRE job was 96 work units. So, A did 56/96 of the work.
This means that A should get 56/96 of the $10,800 payment.
(56/96)(10,800) = (7/12)(10,800)
= $6300
Of course, none of the answer choices match $6300, but that's because we did some estimating/rounding earlier.
The closest answer choice is $6400, so the correct answer must be D
Cheers,
Brent
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The solution below is similar to Brent's, but with one suggestion:
To make the math easier, we can divide all of the times by 4:
Pay per unit = 10800/24 = $450.
A's rate = w/t = 24/6 = 4 units per day.
B's rate = w/t = 24/8 = 3 units per day.
C's rate = w/t = 24/12 = 2 units per day.
Work produced by A on the first day = 4 units.
Work produced by A on the second day = 4 units.
Work produced by B on the second day = 3 units.
Remaining work = 24-4-4-3 = 13 units.
When A, B and C work together, their combined rate = 4+3+2 = 9 units, of which 4 will be produced by A.
Thus, A will produces 4/9 of the remaining 13 units:
(4/9) * 13 = 52/9 ≈ 6.
Total number of units produced by A ≈ 4+4+6 = 14.
Thus:
A's pay ≈ 14*450 ≈ 6300.
The correct answer is D.
Please note that A's exact pay = $6200 (not $6400 as indicated in the problem as posted above):
(4 + 4 + 52/9) * 450 = 6200.
To make the math easier, we can divide all of the times by 4:
Let the job = the LCM of 6, 8 and 12 = 24 units.A, B and C working alone can complete a work in 6, 8, and 12 days respectively. "A" started the work and "B" joined him after 1 day and "C" joined them after 1 more day. If they were paid $10,800 for the work done, how much did "A" get ?
(A) 2800
(B) 3600
(C) 5400
(D) 6200
(E) 7600
Pay per unit = 10800/24 = $450.
A's rate = w/t = 24/6 = 4 units per day.
B's rate = w/t = 24/8 = 3 units per day.
C's rate = w/t = 24/12 = 2 units per day.
Work produced by A on the first day = 4 units.
Work produced by A on the second day = 4 units.
Work produced by B on the second day = 3 units.
Remaining work = 24-4-4-3 = 13 units.
When A, B and C work together, their combined rate = 4+3+2 = 9 units, of which 4 will be produced by A.
Thus, A will produces 4/9 of the remaining 13 units:
(4/9) * 13 = 52/9 ≈ 6.
Total number of units produced by A ≈ 4+4+6 = 14.
Thus:
A's pay ≈ 14*450 ≈ 6300.
The correct answer is D.
Please note that A's exact pay = $6200 (not $6400 as indicated in the problem as posted above):
(4 + 4 + 52/9) * 450 = 6200.
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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.
For more information, please email me (Mitch Hunt) at [email protected].
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