Efficiency of B is 40% more than efficiency of A and efficiency of C is 150% of efficiency of B. B alone can complete 40% of work in 6 days. Then, find in how many days 60% of the same work will be completed by A & C working together, if A is working with 5% more efficiency.

Options

A. 4 days
B. 6 days
C. 5 days
D. 3 days

Answer

To solve the problem step by step, we will follow the information given in the question and derive the required values systematically.

### Step 1: Determine the Efficiency of A, B, and C

Let the efficiency of A be \( E_A \).

Since the efficiency of B is 40% more than A:
\[ E_B = E_A + 0.4E_A = 1.4E_A \]

The efficiency of C is 150% of B:
\[ E_C = 1.5E_B = 1.5 \times 1.4E_A = 2.1E_A \]

### Step 2: Calculate the Total Work

B can complete 40% of the work in 6 days. Therefore, the total work can be calculated as follows:
\[ \text{If } 40\% \text{ of work is done in 6 days, then } 100\% \text{ of work will take } \frac{6 \text{ days}}{0.4} = 15 \text{ days.} \]

### Step 3: Calculate the Total Work in Terms of Efficiency

Now, we can calculate the total work (W):
\[ W = \text{Total Time} \times \text{Efficiency of B} = 15 \times E_B \]
Substituting \( E_B = 1.4E_A \):
\[ W = 15 \times 1.4E_A = 21E_A \]

### Step 4: Calculate the Efficiency of A with 5% Increase

A's efficiency is increased by 5%:
\[ E_A' = E_A + 0.05E_A = 1.05E_A \]

### Step 5: Calculate the Combined Efficiency of A and C

Now, we can calculate the combined efficiency of A and C:
\[ E_{A+C} = E_A' + E_C = 1.05E_A + 2.1E_A = 3.15E_A \]

### Step 6: Calculate the Work to be Done

We need to find out how much work corresponds to 60% of the total work:
\[ \text{Required Work} = 0.6W = 0.6 \times 21E_A = 12.6E_A \]

### Step 7: Calculate the Time Taken by A and C to Complete 60% of Work

Using the formula for time:
\[ \text{Time} = \frac{\text{Work}}{\text{Efficiency}} = \frac{12.6E_A}{3.15E_A} \]
The \( E_A \) cancels out:
\[ \text{Time} = \frac{12.6}{3.15} = 4 \text{ days} \]

### Conclusion

Therefore, A and C working together can complete 60% of the work in **4 days**.

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