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A B can do a piece of work in 12 days. While B C in 20/3 days. Work is complete by A,B and C by working 3,4and 7 days respectively. Find in how many days A alone complete whole work? a) 15 b) 20 c) 25 d) 30?
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? A B can do a piece of work in 12 days. While B C in 20/3 days. Work ...
Solution:
Given, A and B can do a piece of work in 12 days while B and C can do the same work in 20/3 days.
Let us assume that the total work is equal to LCM of 12 and 20/3, i.e., 20 units.
Then, A, B, and C can do the work in 20/12, 20/12, and 20/(20/3) days respectively.
Simplifying the above expressions, we get:
A can complete the work in 5/3 days.
B can complete the work in 5 days.
C can complete the work in 3 days.
Let us assume that A alone can complete the work in x days.
Now, as per the question, A, B, and C work together for 3, 4, and 7 days respectively.
Therefore, the amount of work done by them will be:
Work done by A, B, and C in 3 days = 3(5/3 + 1/5 + 1/3) = 20/3
Work done by A, B, and C in 4 days = 4(5/3 + 1/5 + 1/3) = 80/15
Work done by A, B, and C in 7 days = 7(5/3 + 1/5 + 1/3) = 140/15
Now, the remaining work will be equal to the total work minus the work done by A, B, and C in 3, 4, and 7 days respectively.
Therefore, the remaining work will be:
20 - 20/3 = 40/3 units
20 - 80/15 = 20/3 units
20 - 140/15 = 20/3 units
Now, we can find the value of x by using the remaining work and the time taken by A alone to complete the work.
So, we get:
(40/3)/x + 3(5/3) = 20
(20/3)/x + 4(5/3) = 20
(20/3)/x + 7(5/3) = 20
Solving the above equations, we get:
x = 15 days
Therefore, A alone can complete the whole work in 15 days.
Hence, the correct option is (a) 15.
Given, A and B can do a piece of work in 12 days while B and C can do the same work in 20/3 days.
Let us assume that the total work is equal to LCM of 12 and 20/3, i.e., 20 units.
Then, A, B, and C can do the work in 20/12, 20/12, and 20/(20/3) days respectively.
Simplifying the above expressions, we get:
A can complete the work in 5/3 days.
B can complete the work in 5 days.
C can complete the work in 3 days.
Let us assume that A alone can complete the work in x days.
Now, as per the question, A, B, and C work together for 3, 4, and 7 days respectively.
Therefore, the amount of work done by them will be:
Work done by A, B, and C in 3 days = 3(5/3 + 1/5 + 1/3) = 20/3
Work done by A, B, and C in 4 days = 4(5/3 + 1/5 + 1/3) = 80/15
Work done by A, B, and C in 7 days = 7(5/3 + 1/5 + 1/3) = 140/15
Now, the remaining work will be equal to the total work minus the work done by A, B, and C in 3, 4, and 7 days respectively.
Therefore, the remaining work will be:
20 - 20/3 = 40/3 units
20 - 80/15 = 20/3 units
20 - 140/15 = 20/3 units
Now, we can find the value of x by using the remaining work and the time taken by A alone to complete the work.
So, we get:
(40/3)/x + 3(5/3) = 20
(20/3)/x + 4(5/3) = 20
(20/3)/x + 7(5/3) = 20
Solving the above equations, we get:
x = 15 days
Therefore, A alone can complete the whole work in 15 days.
Hence, the correct option is (a) 15.
Community Answer
? A B can do a piece of work in 12 days. While B C in 20/3 days. Work ...
Acc to ques,
(A+B)=1/12
(B+C)=3/20
A one day work=1/3
B one day work=1/4
C one day work=1/7
now,
A's 3 day work+ B's 1 day work+C's 6 day work=1
(A+B)×3+(B+C)×1+C's 6 day work=1
3/12 + 3/20 + C's 6 day work=1
C's 6 day work=1-[3/12+3/20]=6/10
C's 1 day work=6/10×1/6=1/10
C will complete whole work alone in 10 days.
then,
A-C=1/12-3/20
A=1/12-3/20+1/10
A=1/30
A alone will complete the whole work in 30 days.
(A+B)=1/12
(B+C)=3/20
A one day work=1/3
B one day work=1/4
C one day work=1/7
now,
A's 3 day work+ B's 1 day work+C's 6 day work=1
(A+B)×3+(B+C)×1+C's 6 day work=1
3/12 + 3/20 + C's 6 day work=1
C's 6 day work=1-[3/12+3/20]=6/10
C's 1 day work=6/10×1/6=1/10
C will complete whole work alone in 10 days.
then,
A-C=1/12-3/20
A=1/12-3/20+1/10
A=1/30
A alone will complete the whole work in 30 days.
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? A B can do a piece of work in 12 days. While B C in 20/3 days. Work is complete by A,B and C by working 3,4and 7 days respectively. Find in how many days A alone complete whole work? a) 15 b) 20 c) 25 d) 30?
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? A B can do a piece of work in 12 days. While B C in 20/3 days. Work is complete by A,B and C by working 3,4and 7 days respectively. Find in how many days A alone complete whole work? a) 15 b) 20 c) 25 d) 30? for CLAT 2024 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about ? A B can do a piece of work in 12 days. While B C in 20/3 days. Work is complete by A,B and C by working 3,4and 7 days respectively. Find in how many days A alone complete whole work? a) 15 b) 20 c) 25 d) 30? covers all topics & solutions for CLAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ? A B can do a piece of work in 12 days. While B C in 20/3 days. Work is complete by A,B and C by working 3,4and 7 days respectively. Find in how many days A alone complete whole work? a) 15 b) 20 c) 25 d) 30?.
? A B can do a piece of work in 12 days. While B C in 20/3 days. Work is complete by A,B and C by working 3,4and 7 days respectively. Find in how many days A alone complete whole work? a) 15 b) 20 c) 25 d) 30? for CLAT 2024 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about ? A B can do a piece of work in 12 days. While B C in 20/3 days. Work is complete by A,B and C by working 3,4and 7 days respectively. Find in how many days A alone complete whole work? a) 15 b) 20 c) 25 d) 30? covers all topics & solutions for CLAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ? A B can do a piece of work in 12 days. While B C in 20/3 days. Work is complete by A,B and C by working 3,4and 7 days respectively. Find in how many days A alone complete whole work? a) 15 b) 20 c) 25 d) 30?.
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