Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?a)2b)3c)4d)6e)8Correct answer is option 'B'. Can you explain this answer?

Question

Answer

If each machine works at a rate of "x" days to complete the job individually, the equation representing the work rate of six machines becomes:

1/x + 1/x + 1/x + 1/x + 1/x + 1/x = 1/12

Simplifying this equation, we find:

6/x = 1/12

Solving for "x", we get:

x = 72

Now, let "y" represent the number of machines needed to complete the job in 8 days. The equation representing the work rate of all machines becomes:

y/72 = 1/8

Simplifying this equation, we find:

y = 9

To determine the additional number of machines required, we subtract the initial number of machines (6) from the required number of machines (9):

required = y - x = 3

Therefore, the answer is B. 3.

Answer

Given:
- 6 machines can complete a job in 12 days
- All machines work at the same constant rate

To find:
- How many additional machines are needed to complete the job in 8 days

Let's assume that one machine completes 1 unit of work in 1 day. Therefore, the total work required to complete the job is 6 units (6 machines * 12 days).

Step 1: Find the rate of each machine
Since all machines work at the same constant rate, each machine completes 1/12th of the job in 1 day.

Step 2: Find the rate of all machines combined
Since there are 6 machines, the combined rate of all machines is 6 * 1/12 = 1/2 units per day.

Step 3: Find the work remaining after 8 days
In 8 days, the machines working at the same rate will complete 8 * 1/2 = 4 units of work (since the combined rate is 1/2 units per day).

Step 4: Find the additional machines required to complete the remaining work in 8 days
The remaining work is 6 - 4 = 2 units.
To complete the remaining work in 8 days, each additional machine needs to work at the same rate of 1/2 units per day.

Let's assume the number of additional machines required is x.
Therefore, the combined rate of all machines would be (6 + x) * 1/2 units per day.

Step 5: Set up the equation
To complete 2 units of work in 8 days, the equation becomes:
2 = 8 * (6 + x) * 1/2

Step 6: Solve for x
2 = 8 * (6 + x) * 1/2
2 = 4(6 + x)
2 = 24 + 4x
4x = 2 - 24
4x = -22
x = -22/4
x = -11/2

Since the number of machines cannot be negative, we discard the negative solution.

Therefore, the number of additional machines required to complete the job in 8 days is 3 (option B).

Similar GMAT Doubts

If two copying machines work simultaneously at their respective constant rates, how many copies do they produce in 5 minutes?(1) One of the machines produces copies at the constant rate of 250 copies per minute.(2) One of the machines produces copies at twice the constant rate of the other machine.

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