Anu can complete a work in 10 days. Manu is 25% more efficient than Annu and Sonu is 60% more efficient then Manu. Working together, how long would they take to finish the job?

Options

A. `3(5)/(8)` days
B. `5(6)/(7)` days
C. `2(6)/(17)` days
D. None of these

Answer

To solve the problem step by step, we will calculate the efficiencies of Anu, Manu, and Sonu, and then determine how long they will take to complete the work together.

### Step 1: Determine Anu's Work Rate
Anu can complete the work in 10 days. Therefore, her work rate is:
\[ \text{Work rate of Anu} = \frac{1 \text{ work}}{10 \text{ days}} = 0.1 \text{ work per day} \]

### Step 2: Calculate Manu's Work Rate
Manu is 25% more efficient than Anu. To find Manu's efficiency:
\[ \text{Efficiency of Manu} = \text{Efficiency of Anu} \times (1 + 0.25) = 0.1 \times 1.25 = 0.125 \text{ work per day} \]

### Step 3: Calculate Sonu's Work Rate
Sonu is 60% more efficient than Manu. Therefore, Sonu's efficiency is:
\[ \text{Efficiency of Sonu} = \text{Efficiency of Manu} \times (1 + 0.60) = 0.125 \times 1.6 = 0.2 \text{ work per day} \]

### Step 4: Calculate Total Work Rate When Working Together
Now, we can find the total work rate when Anu, Manu, and Sonu work together:
\[ \text{Total efficiency} = \text{Efficiency of Anu} + \text{Efficiency of Manu} + \text{Efficiency of Sonu} \]
\[ \text{Total efficiency} = 0.1 + 0.125 + 0.2 = 0.425 \text{ work per day} \]

### Step 5: Calculate Time to Complete the Work
Assuming the total work is 1 unit, the time taken to complete the work when they work together is:
\[ \text{Time} = \frac{\text{Total work}}{\text{Total efficiency}} = \frac{1 \text{ work}}{0.425 \text{ work per day}} \approx 2.3529 \text{ days} \]

To express this in a more understandable format:
\[ \text{Time} \approx 2 \text{ days and } 0.3529 \text{ days} \]
Converting 0.3529 days into hours (1 day = 24 hours):
\[ 0.3529 \times 24 \approx 8.47 \text{ hours} \]

### Final Answer
Thus, Anu, Manu, and Sonu together will take approximately 2 days and 8.47 hours to finish the work.

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