Anurag is 40% less efficient than Bholu, who can do the same work in 20% less time than Chotu. If Anurag and Bholu together can complete 80% of work in 12 days, then in how many days 60% of work can be completed by Bholu and Chotu together.

Options

A. A)2 days
B. B)4 days
C. C)6 days
D. D)8 days

Answer

To solve the problem step by step, we will analyze the efficiencies of Anurag, Bholu, and Chotu, and then calculate the required time for Bholu and Chotu to complete 60% of the work.

### Step 1: Determine the efficiency of Anurag and Bholu
Anurag is 40% less efficient than Bholu. If we assume Bholu's efficiency is 5 units, then Anurag's efficiency can be calculated as follows:

\[ \text{Anurag's efficiency} = 5 - (0.4 \times 5) = 5 - 2 = 3 \text{ units} \]

### Step 2: Determine the efficiency of Chotu
Bholu can do the same work in 20% less time than Chotu. This means if Chotu takes 5 units of time, Bholu takes 4 units of time. The ratio of their efficiencies is the inverse of the ratio of their times:

\[ \text{Efficiency ratio of Bholu to Chotu} = \frac{5}{4} \]

Thus, if Bholu's efficiency is 5 units, Chotu's efficiency can be calculated as:

\[ \text{Chotu's efficiency} = 4 \text{ units} \]

### Step 3: Calculate the total work done by Anurag and Bholu
Anurag and Bholu together can complete 80% of the work in 12 days. Their combined efficiency is:

\[ \text{Total efficiency of Anurag and Bholu} = 3 + 5 = 8 \text{ units} \]

The total work (W) can be calculated using the formula:

\[ \text{Work} = \text{Efficiency} \times \text{Time} \]

Given that they complete 80% of the total work in 12 days:

\[ \frac{4}{5}W = 8 \times 12 \]

Calculating the right side:

\[ \frac{4}{5}W = 96 \implies W = 96 \times \frac{5}{4} = 120 \text{ units} \]

### Step 4: Calculate the time taken by Bholu and Chotu to complete 60% of the work
Now we need to find out how many days Bholu and Chotu will take to complete 60% of the total work.

60% of the total work is:

\[ \text{Work to be done} = 0.6 \times 120 = 72 \text{ units} \]

The combined efficiency of Bholu and Chotu is:

\[ \text{Total efficiency of Bholu and Chotu} = 5 + 4 = 9 \text{ units} \]

Now, we can calculate the time (T) taken by Bholu and Chotu to complete 72 units of work:

\[ T = \frac{\text{Work}}{\text{Efficiency}} = \frac{72}{9} = 8 \text{ days} \]

### Final Answer
Thus, Bholu and Chotu together can complete 60% of the work in **8 days**.

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