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Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?
Correct answer is '13'. Can you explain this answer?
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Three men and eight machines can finish a job in half the time taken ...
Consider the work done by a man in a day = a and that by a machine = b
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Since, three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job, hence the efficiency will be double.
=> 3a+8b = 2(3b+8a)
=>13a=2b
Hence work done by 13 men in a day = work done by 2 machines in a day.
=> If two machines can finish the job in 13 days, then same work will be done 13 men in 13 days.
Hence the required number of men = 13
Most Upvoted Answer
Three men and eight machines can finish a job in half the time taken ...
Given information:
- Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job.
- Two machines can finish the job in 13 days.
To find:
- How many men can finish the job in 13 days?
Assumptions:
- The amount of work done by each machine or man is constant.
Solution:
Let's assume:
- The amount of work done by one machine in one day is "M" units.
- The amount of work done by one man in one day is "N" units.
Step 1: Calculate the work done by two machines in 13 days:
- Two machines can finish the job in 13 days.
- So, the work done by two machines in 13 days = 2 x 13M = 26M units.
Step 2: Calculate the work done by three men and eight machines in a certain time:
- Let's assume the time taken by three men and eight machines to finish the job is "T" days.
- The work done by three men and eight machines in "T" days = (3N x T) + (8M x T) = (3N + 8M)T units.
Step 3: Calculate the work done by three machines and eight men in the same time:
- The work done by three machines and eight men in "T" days = (3M x T) + (8N x T) = (3M + 8N)T units.
Step 4: Use the given information to form an equation:
- According to the given information, the work done by three men and eight machines in "T" days is half the work done by three machines and eight men in the same time.
- (3N + 8M)T = 0.5 x (3M + 8N)T
- 3N + 8M = 0.5 x (3M + 8N)
Step 5: Use the given information to form another equation:
- According to the given information, the work done by two machines in 13 days is equal to the work done by three machines and eight men in a certain time.
- 2 x 13M = (3M + 8N)T
- 26M = (3M + 8N)T
Step 6: Solve the two equations:
We have two equations:
1) 3N + 8M = 0.5 x (3M + 8N)
2) 26M = (3M + 8N)T
By solving these equations, we get:
- N = 4M
- T = 13
Therefore, the number of men required to finish the job in 13 days is 13.
- Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job.
- Two machines can finish the job in 13 days.
To find:
- How many men can finish the job in 13 days?
Assumptions:
- The amount of work done by each machine or man is constant.
Solution:
Let's assume:
- The amount of work done by one machine in one day is "M" units.
- The amount of work done by one man in one day is "N" units.
Step 1: Calculate the work done by two machines in 13 days:
- Two machines can finish the job in 13 days.
- So, the work done by two machines in 13 days = 2 x 13M = 26M units.
Step 2: Calculate the work done by three men and eight machines in a certain time:
- Let's assume the time taken by three men and eight machines to finish the job is "T" days.
- The work done by three men and eight machines in "T" days = (3N x T) + (8M x T) = (3N + 8M)T units.
Step 3: Calculate the work done by three machines and eight men in the same time:
- The work done by three machines and eight men in "T" days = (3M x T) + (8N x T) = (3M + 8N)T units.
Step 4: Use the given information to form an equation:
- According to the given information, the work done by three men and eight machines in "T" days is half the work done by three machines and eight men in the same time.
- (3N + 8M)T = 0.5 x (3M + 8N)T
- 3N + 8M = 0.5 x (3M + 8N)
Step 5: Use the given information to form another equation:
- According to the given information, the work done by two machines in 13 days is equal to the work done by three machines and eight men in a certain time.
- 2 x 13M = (3M + 8N)T
- 26M = (3M + 8N)T
Step 6: Solve the two equations:
We have two equations:
1) 3N + 8M = 0.5 x (3M + 8N)
2) 26M = (3M + 8N)T
By solving these equations, we get:
- N = 4M
- T = 13
Therefore, the number of men required to finish the job in 13 days is 13.
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Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?Correct answer is '13'. Can you explain this answer?
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