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02 Jan 2021, 11:11
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Working together at their respective rates, machine A, B, and C can finish a certain work in 8/3 hours. How many hours will it take A to finish the work independently?
(1) Working together, A and B can finish the work in 4 hours.
(2) Working together, B and C can finish the work in 48/7 hours.
(1) Working together, A and B can finish the work in 4 hours.
(2) Working together, B and C can finish the work in 48/7 hours.
Shadyshades
Joined: 02 Nov 2020
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02 Jan 2021, 13:44
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In one hour A,B and C can finish 3/8 work
Mathematically, 1/A +1/B +1/C = 3/8 ( Main equation)
We need to find the number of hours A take to complete its work.
Statement 1-
In one hour, 1/A+1/B = 1/4
With this, i can calculate only C but not B or A.
Not sufficient.
Statement 2 -
1/B+1/C= 7/48
With this, i can calculate A by putting in main equation.
Sufficient.
Option B
Mathematically, 1/A +1/B +1/C = 3/8 ( Main equation)
We need to find the number of hours A take to complete its work.
Statement 1-
In one hour, 1/A+1/B = 1/4
With this, i can calculate only C but not B or A.
Not sufficient.
Statement 2 -
1/B+1/C= 7/48
With this, i can calculate A by putting in main equation.
Sufficient.
Option B
03 Jan 2021, 00:24
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From question stem
Working together at their respective rates, machine A, B, and C can finish a certain work in 8/3 hours.
Working alone, if A took A hours, B took B hours and C took C hours to complete the work, in an hour A will complete \(\frac{1}{A}\) of the work, B will complete \(\frac{1}{B}\) of the work and C will complete \(\frac{1}{C}\) of the work.
So, A, B, and C working together will, in an hour, complete \(\frac{1}{A} + \frac{1}{B} + \frac{1}{C}\) of the work ... (1)
If the machines together take \(\frac{8}{3}\) hours to complete the work, they will complete \(\frac{3}{8}\) of the work in an hour .... (2)
Equating (1) and (2), we get \(\frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{3}{8}\) ... (3).
Statement 1: Working together, A and B can finish the work in 4 hours.
i.e., \(\frac{1}{A} + \frac{1}{B} = \frac{1}{4}\) ... (4)
Solving (3) and (4) will give us a unique value for C. But we will not get a unique value for A.
Statement 1 alone is NOT sufficient. Eliminate options A and D.
Statement 2: Working together, B and C can finish the work in 48/7 hours.
i.e., i.e., \(\frac{1}{B} + \frac{1}{C} = \frac{7}{48}\) ... (5)
Solving (3) and (5) will give us a unique value for A.
Statement 2 alone is sufficient.
Choice B is the answer.
Working together at their respective rates, machine A, B, and C can finish a certain work in 8/3 hours.
Working alone, if A took A hours, B took B hours and C took C hours to complete the work, in an hour A will complete \(\frac{1}{A}\) of the work, B will complete \(\frac{1}{B}\) of the work and C will complete \(\frac{1}{C}\) of the work.
So, A, B, and C working together will, in an hour, complete \(\frac{1}{A} + \frac{1}{B} + \frac{1}{C}\) of the work ... (1)
If the machines together take \(\frac{8}{3}\) hours to complete the work, they will complete \(\frac{3}{8}\) of the work in an hour .... (2)
Equating (1) and (2), we get \(\frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{3}{8}\) ... (3).
Statement 1: Working together, A and B can finish the work in 4 hours.
i.e., \(\frac{1}{A} + \frac{1}{B} = \frac{1}{4}\) ... (4)
Solving (3) and (4) will give us a unique value for C. But we will not get a unique value for A.
Statement 1 alone is NOT sufficient. Eliminate options A and D.
Statement 2: Working together, B and C can finish the work in 48/7 hours.
i.e., i.e., \(\frac{1}{B} + \frac{1}{C} = \frac{7}{48}\) ... (5)
Solving (3) and (5) will give us a unique value for A.
Statement 2 alone is sufficient.
Choice B is the answer.
