Two spinning machines A and B can together produce 50000 m of cloth in 20 hours. If machine B alone can produce the same amount of cloth in 25 hours, then how much cloth can machine A produce alone in 20 hours?

Options

A. 18000 m
B. 15000 m
C. 10000 m
D. 25000 m

Answer

To solve the problem, we need to find out how much cloth machine A can produce alone in 20 hours, given the combined production of machines A and B, as well as the production rate of machine B alone.

### Step 1: Determine the combined rate of machines A and B.
We know that together, machines A and B can produce 50,000 meters of cloth in 20 hours.

To find their combined rate of production, we can use the formula:
\[ \text{Rate of A and B} = \frac{\text{Total Cloth Produced}}{\text{Total Time}} = \frac{50000 \text{ m}}{20 \text{ hours}} = 2500 \text{ m/hour} \]

### Step 2: Determine the rate of machine B.
Machine B can produce the same amount of cloth (50,000 meters) in 25 hours.

Using the same formula, we find the rate of machine B:
\[ \text{Rate of B} = \frac{50000 \text{ m}}{25 \text{ hours}} = 2000 \text{ m/hour} \]

### Step 3: Calculate the rate of machine A.
Now that we have the combined rate of machines A and B, and the rate of machine B, we can find the rate of machine A.

Using the equation:
\[ \text{Rate of A} = \text{Rate of A and B} - \text{Rate of B} \]
Substituting the values we found:
\[ \text{Rate of A} = 2500 \text{ m/hour} - 2000 \text{ m/hour} = 500 \text{ m/hour} \]

### Step 4: Calculate the total cloth produced by machine A in 20 hours.
Now that we have the rate of machine A, we can find out how much cloth it can produce in 20 hours:
\[ \text{Cloth produced by A in 20 hours} = \text{Rate of A} \times \text{Time} = 500 \text{ m/hour} \times 20 \text{ hours} = 10000 \text{ m} \]

### Final Answer:
Machine A can produce **10,000 meters** of cloth alone in 20 hours.

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