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Manish, Mukesh and Sachin are Accountant...

Manish, Mukesh and Sachin are Accountants. Mukesh can file a return in 5 hours and Sachin in 4 hours alone. All three together can do it in 2 hours. In what time (in hrs) will Manish do the work?
A. 15 B. 20 C. 17 D. 10

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Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find out how long Manish will take to file a return by himself. We know the following: 1. Mukesh can file a return in 5 hours. 2. Sachin can file a return in 4 hours. 3. All three together can file a return in 2 hours. ### Step-by-Step Solution: **Step 1: Calculate the work done by Mukesh and Sachin in one hour.** - Mukesh's work rate = 1 return / 5 hours = 1/5 returns per hour. - Sachin's work rate = 1 return / 4 hours = 1/4 returns per hour. **Step 2: Calculate the combined work rate of Mukesh and Sachin.** - Combined work rate of Mukesh and Sachin = (1/5 + 1/4) returns per hour. To add these fractions, we need a common denominator: - The least common multiple (LCM) of 5 and 4 is 20. So, we convert the fractions: - Mukesh's work rate = 1/5 = 4/20 - Sachin's work rate = 1/4 = 5/20 Now, adding them together: \[ \text{Combined work rate of Mukesh and Sachin} = \frac{4}{20} + \frac{5}{20} = \frac{9}{20} \text{ returns per hour.} \] **Step 3: Calculate the combined work rate of all three accountants.** - We know that all three together can complete 1 return in 2 hours, which means their combined work rate is: \[ \text{Combined work rate of Manish, Mukesh, and Sachin} = \frac{1}{2} \text{ returns per hour.} \] **Step 4: Set up the equation to find Manish's work rate.** Let Manish's work rate be \( M \) returns per hour. From the previous steps, we have: \[ M + \frac{9}{20} = \frac{1}{2} \] **Step 5: Convert \(\frac{1}{2}\) to a fraction with a denominator of 20.** \[ \frac{1}{2} = \frac{10}{20} \] Now, substituting back into the equation: \[ M + \frac{9}{20} = \frac{10}{20} \] **Step 6: Solve for \( M \).** \[ M = \frac{10}{20} - \frac{9}{20} = \frac{1}{20} \text{ returns per hour.} \] **Step 7: Calculate the time taken by Manish to complete the work alone.** If Manish's work rate is \( \frac{1}{20} \) returns per hour, then the time taken by Manish to complete 1 return is: \[ \text{Time} = \frac{1 \text{ return}}{M} = \frac{1}{\frac{1}{20}} = 20 \text{ hours.} \] ### Conclusion: Manish will take **20 hours** to file the return alone.
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