A work is done by three person A,B and C. A alone takes 10 hours to complete a single product but B and C working together takes 4 hours, for the completion of the same product. If all of them worked together and completed 14 products. Then how many hours have they worked?

Options

A. 20 hrs
B. 28 hrs
C. 40 hrs
D. 54 hrs

Answer

To solve the problem step by step, let's break down the information provided and calculate how many hours A, B, and C worked together to complete 14 products.

### Step 1: Determine the work done by A, B, and C

1. **A's Work Rate**: A alone takes 10 hours to complete 1 product. Therefore, A's work rate is:
\[ \text{Work Rate of A} = \frac{1 \text{ product}}{10 \text{ hours}} = 0.1 \text{ products/hour} \]

2. **B and C's Work Rate**: B and C together take 4 hours to complete 1 product. Therefore, their combined work rate is:
\[ \text{Work Rate of B and C} = \frac{1 \text{ product}}{4 \text{ hours}} = 0.25 \text{ products/hour} \]

### Step 2: Calculate the combined work rate of A, B, and C

3. **Combined Work Rate**: The combined work rate of A, B, and C is the sum of their individual work rates:
\[ \text{Combined Work Rate} = \text{Work Rate of A} + \text{Work Rate of B and C} \]
\[ = 0.1 + 0.25 = 0.35 \text{ products/hour} \]

### Step 3: Calculate the time taken to complete 1 product

4. **Time to complete 1 product**: The time taken to complete 1 product by all three working together is the reciprocal of their combined work rate:
\[ \text{Time for 1 product} = \frac{1 \text{ product}}{0.35 \text{ products/hour}} \approx 2.857 \text{ hours} \]

### Step 4: Calculate the time taken to complete 14 products

5. **Total time for 14 products**: To find the total time taken to complete 14 products, multiply the time taken for 1 product by 14:
\[ \text{Total Time} = 14 \times 2.857 \approx 40 \text{ hours} \]

### Conclusion

Thus, A, B, and C worked together for **40 hours** to complete 14 products.

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