Question

Running at the constant rate, ten identical machines can produce 1000 plates per minute. At this rate, how many plates could 25 such machines can produce in 5 minutes?

• A. 12500
• B. 12000
• C. 10000
• D. 13000

Hint:

In work-rate problems, always find the "unit rate" first – the amount of work done by one person/machine in one unit of time (e.g., plates per machine per minute). Once you have this base rate, you can easily calculate the output for any number of machines over any period.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
This is a problem of work and rate, which can be solved using proportionality. The number of plates produced is directly proportional to the number of machines and the time they run.

Step 2: Key Formula or Approach
The core idea is to find the production rate of a single machine first.
Rate of 1 machine = (Total plates produced) / (Number of machines \(\times\) Time)
Total Production = (Rate of 1 machine) \(\times\) (Number of new machines) \(\times\) (New time)

Step 3: Detailed Explanation
\begin{enumerate}
Find the rate of one machine:
Given: 10 machines produce 1000 plates in 1 minute.
So, the rate of 1 machine is: \[ \text{Rate}_1 = \frac{1000 \text{ plates}}{10 \text{ machines} \times 1 \text{ minute}} = 100 \text{ plates per machine per minute} \]
Calculate the production for 25 machines in 5 minutes:
Now, we use the rate of one machine to find the total output for the new conditions.
Number of machines = 25
Time = 5 minutes
Total Plates = (Rate of 1 machine) \(\times\) (Number of machines) \(\times\) (Time) \[ \text{Total Plates} = 100 \frac{\text{plates}}{\text{machine} \cdot \text{minute}} \times 25 \text{ machines} \times 5 \text{ minutes} \] \[ \text{Total Plates} = 100 \times 25 \times 5 \] \[ \text{Total Plates} = 2500 \times 5 \] \[ \text{Total Plates} = 12500 \] \end{enumerate}
Step 4: Final Answer
At this rate, 25 such machines can produce 12,500 plates in 5 minutes. Therefore, option (A) is the correct answer.