Veer is 40% less efficient than Bhavya and both complete the work together in 30 days, if Abhishek takes 10 days less as Veer and Bhavya takes together. Then find how many days will be required to complete the work, if all three work together?

Options

A. 16 days
B. 12 days
C. 10 days
D. 8 days

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the efficiencies of Veer and Bhavya.
Let Bhavya's efficiency be 100 units of work per day. Since Veer is 40% less efficient than Bhavya, we can calculate Veer's efficiency as follows:

\[ \text{Veer's efficiency} = 100 - (40\% \text{ of } 100) = 100 - 40 = 60 \text{ units of work per day.} \]

### Step 2: Calculate the combined efficiency of Veer and Bhavya.
The combined efficiency of Veer and Bhavya is:

\[ \text{Combined efficiency} = \text{Bhavya's efficiency} + \text{Veer's efficiency} = 100 + 60 = 160 \text{ units of work per day.} \]

### Step 3: Calculate the total work done.
Since Veer and Bhavya together complete the work in 30 days, we can calculate the total work as follows:

\[ \text{Total Work} = \text{Combined efficiency} \times \text{Time} = 160 \text{ units/day} \times 30 \text{ days} = 4800 \text{ units.} \]

### Step 4: Determine the time taken by Abhishek.
We know that Abhishek takes 10 days less than the time taken by Veer and Bhavya together. The time taken by Veer and Bhavya together is 30 days, so:

\[ \text{Time taken by Abhishek} = 30 - 10 = 20 \text{ days.} \]

### Step 5: Calculate Abhishek's efficiency.
Using the total work calculated earlier, we can find Abhishek's efficiency:

\[ \text{Abhishek's efficiency} = \frac{\text{Total Work}}{\text{Time taken by Abhishek}} = \frac{4800 \text{ units}}{20 \text{ days}} = 240 \text{ units of work per day.} \]

### Step 6: Calculate the total efficiency of all three working together.
Now, we can find the total efficiency when all three work together:

\[ \text{Total efficiency} = \text{Bhavya's efficiency} + \text{Veer's efficiency} + \text{Abhishek's efficiency} = 100 + 60 + 240 = 400 \text{ units of work per day.} \]

### Step 7: Calculate the time required for all three to complete the work together.
Finally, we can find out how many days it will take for all three to complete the total work together:

\[ \text{Time required} = \frac{\text{Total Work}}{\text{Total efficiency}} = \frac{4800 \text{ units}}{400 \text{ units/day}} = 12 \text{ days.} \]

### Final Answer:
Thus, the time required for all three to complete the work together is **12 days**.

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