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A, B and C are assigned a piece of work which they can complete by working together in 15 days. Their efficiencies (measured in terms of rate of doing work) are in the ratio 1 : 2 : 3. After 1/3 of the work is completed, one of them has to be withdrawn due to budget constraint. Their wages per day are in the ratio 3 : 5 : 6. The number of days in which the remaining two persons can complete the work (at optimal cost) is:
- a)18
- b)20
- c)15
- d)12
- e)17
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A, B and C are assigned a piece of work which they can complete by wo...
Given:
- A, B, and C can complete a piece of work together in 15 days.
- Their efficiencies are in the ratio 1:2:3.
- After completing 1/3 of the work, one person has to be withdrawn due to budget constraints.
- Their wages per day are in the ratio 3:5:6.
To find:
The number of days in which the remaining two persons can complete the work at optimal cost.
Solution:
Let the efficiencies of A, B, and C be x, 2x, and 3x respectively.
Efficiency is inversely proportional to the number of days taken to complete the work. Therefore, the number of days taken by A, B, and C to complete the work individually will be 15x, 7.5x, and 5x respectively.
Step 1: Calculating the cost per day for each person:
Let the wages per day of A, B, and C be 3y, 5y, and 6y respectively.
The cost per day for A = 3y / 15x = y / 5x
The cost per day for B = 5y / 7.5x = 2y / 3x
The cost per day for C = 6y / 5x = 6y / 5x
Step 2: Calculating the cost of completing 1/3rd of the work:
Let the total work be W. Then 1/3rd of the work = W/3.
The work done by A, B, and C individually in completing 1/3rd of the work is:
Work done by A = (W/3) * (1/15x) = W/45x
Work done by B = (W/3) * (1/7.5x) = W/22.5x
Work done by C = (W/3) * (1/5x) = W/15x
Step 3: Calculating the cost for completing 1/3rd of the work:
The cost for completing 1/3rd of the work is:
Cost for A = (W/45x) * (y/5x) = Wy / 225x^2
Cost for B = (W/22.5x) * (2y/3x) = 2Wy / 67.5x^2
Cost for C = (W/15x) * (6y/5x) = 6Wy / 75x^2
Step 4: Calculating the remaining work:
The remaining work after completing 1/3rd of the work is:
Remaining work = W - (W/3) = 2W/3
Step 5: Calculating the number of days required to complete the remaining work:
The remaining work can be completed by two people with optimal cost.
Let the efficiencies of the remaining two people be 2x and 3x respectively (after one person is withdrawn).
The number of days taken by the remaining two people to complete the remaining work is:
Number of days = (2W/3) / (2x +
- A, B, and C can complete a piece of work together in 15 days.
- Their efficiencies are in the ratio 1:2:3.
- After completing 1/3 of the work, one person has to be withdrawn due to budget constraints.
- Their wages per day are in the ratio 3:5:6.
To find:
The number of days in which the remaining two persons can complete the work at optimal cost.
Solution:
Let the efficiencies of A, B, and C be x, 2x, and 3x respectively.
Efficiency is inversely proportional to the number of days taken to complete the work. Therefore, the number of days taken by A, B, and C to complete the work individually will be 15x, 7.5x, and 5x respectively.
Step 1: Calculating the cost per day for each person:
Let the wages per day of A, B, and C be 3y, 5y, and 6y respectively.
The cost per day for A = 3y / 15x = y / 5x
The cost per day for B = 5y / 7.5x = 2y / 3x
The cost per day for C = 6y / 5x = 6y / 5x
Step 2: Calculating the cost of completing 1/3rd of the work:
Let the total work be W. Then 1/3rd of the work = W/3.
The work done by A, B, and C individually in completing 1/3rd of the work is:
Work done by A = (W/3) * (1/15x) = W/45x
Work done by B = (W/3) * (1/7.5x) = W/22.5x
Work done by C = (W/3) * (1/5x) = W/15x
Step 3: Calculating the cost for completing 1/3rd of the work:
The cost for completing 1/3rd of the work is:
Cost for A = (W/45x) * (y/5x) = Wy / 225x^2
Cost for B = (W/22.5x) * (2y/3x) = 2Wy / 67.5x^2
Cost for C = (W/15x) * (6y/5x) = 6Wy / 75x^2
Step 4: Calculating the remaining work:
The remaining work after completing 1/3rd of the work is:
Remaining work = W - (W/3) = 2W/3
Step 5: Calculating the number of days required to complete the remaining work:
The remaining work can be completed by two people with optimal cost.
Let the efficiencies of the remaining two people be 2x and 3x respectively (after one person is withdrawn).
The number of days taken by the remaining two people to complete the remaining work is:
Number of days = (2W/3) / (2x +
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Community Answer
A, B and C are assigned a piece of work which they can complete by wo...
Let A take x days to complete the work, B x/2 and C x/3.
So, 1/x + 1/(x/2) + 1/(x/3) = 1/15
Solving, 6/x = 1/15 or x = 90.
So A will take 90 days, B 45 days, C 30 days to do the work.
Wages per unit of work for A,B,C are in the ratio: 3/1 : 5/2 : 6/3 = 3:2.5:2
So, A is the most expensive for unit of work, and will be withdrawn.
B & C in 1 day can do 1/45 + 1/30 = 1/18 th of work, or B and C working together will take 18 days to do the complete work
Time taken by B & C to do 2/3 rd of work = 2x18/3 = 12 days
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A, B and C are assigned a piece of work which they can complete by working together in 15 days. Their efficiencies (measured in terms of rate of doing work) are in the ratio 1 : 2 : 3. After 1/3 of the work is completed, one of them has to be withdrawn due to budget constraint. Their wages per day are in the ratio 3 : 5 : 6. The number of days in which the remaining two persons can complete the work (at optimal cost) is:a)18b)20c)15d)12e)17Correct answer is option 'D'. Can you explain this answer?
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