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14 Apr 2022, 07:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
77% (02:24) correct
23%
(02:10)
wrong
based on 52
sessions
History
Date
Time
Result
Not Attempted Yet
To complete a piece of work A and B take 8 days, B and C 12 days. A, B and C take 6 days. A and C will take :
A. 7 Days
B. 7.5 Days
C. 8 Days
D. 8.5 Days
E. 9 Days
A. 7 Days
B. 7.5 Days
C. 8 Days
D. 8.5 Days
E. 9 Days
18 Apr 2022, 09:08
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Let the total work done be 48 units, 48 being a common multiple of 8, 12 and 6 which are the respective times taken by the different groups of people.
Let rate of A = p units per day, rate of B = q units per day and rate of C = r units per day.
Rate of working of A and B = \(\frac{48 }{ 8}\) = 6 units per day.
Therefore, p + q = 6 ----- (1)
Rate of working of B and C = \(\frac{48 }{ 12}\) = 4 units per day.
Therefore, q + r = 4 ---- (2)
Rate of working of A, B and C = \(\frac{48 }{ 6}\) = 8 units per day.
Therefore, p + q + r = 8 ---- (3)
Adding equations (1) and (2) , we have p + 2q + r = 10 ---- (4)
Subtracting equation (3) from (4), we have, q = 2. Substituting the value of q in equation (1) and (2) we have p = 4 and r = 2.
Therefore, rate of working of A and C = p + r = 6 units per day.
Time taken by A and C to do the work = \(\frac{48 }{ 6 }\)= 8 days
The correct answer option is C.
Let rate of A = p units per day, rate of B = q units per day and rate of C = r units per day.
Rate of working of A and B = \(\frac{48 }{ 8}\) = 6 units per day.
Therefore, p + q = 6 ----- (1)
Rate of working of B and C = \(\frac{48 }{ 12}\) = 4 units per day.
Therefore, q + r = 4 ---- (2)
Rate of working of A, B and C = \(\frac{48 }{ 6}\) = 8 units per day.
Therefore, p + q + r = 8 ---- (3)
Adding equations (1) and (2) , we have p + 2q + r = 10 ---- (4)
Subtracting equation (3) from (4), we have, q = 2. Substituting the value of q in equation (1) and (2) we have p = 4 and r = 2.
Therefore, rate of working of A and C = p + r = 6 units per day.
Time taken by A and C to do the work = \(\frac{48 }{ 6 }\)= 8 days
The correct answer option is C.
18 Apr 2022, 22:34
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A + B + C ONE DAY WORK = 1/6
C'S ONE DAY WORK = 1/6-1/8 = 1/24
A'S ONE DAY WORK = 1/6-1/12 = 1/12
A+C ONE DAY WORK = 1/24 + 1/12 = 3/24
A+C CAN COMPLETE THE WORK IN = 24/3 = 8 DAYS
C'S ONE DAY WORK = 1/6-1/8 = 1/24
A'S ONE DAY WORK = 1/6-1/12 = 1/12
A+C ONE DAY WORK = 1/24 + 1/12 = 3/24
A+C CAN COMPLETE THE WORK IN = 24/3 = 8 DAYS
