Anand is 50% more efficient than Bharath and Bharath is 100% more efficient that Chandu. Working together, they can complete a work in 10 days. In how many days can Anand alone do the work?

Answer

To solve the problem step by step, let's define the efficiencies of Anand, Bharath, and Chandu and then find out how long Anand would take to complete the work alone.

### Step 1: Define Efficiencies
Let the efficiency of Chandu be \( C \). According to the problem:
- Bharath is 100% more efficient than Chandu, so Bharath's efficiency \( B \) is:
\[ B = C + 100\% \text{ of } C = C + C = 2C \]

- Anand is 50% more efficient than Bharath, so Anand's efficiency \( A \) is:
\[ A = B + 50\% \text{ of } B = B + \frac{1}{2}B = \frac{3}{2}B \]
Substituting \( B = 2C \):
\[ A = \frac{3}{2} \times 2C = 3C \]

### Step 2: Total Efficiency
Now, we can find the total efficiency of Anand, Bharath, and Chandu when they work together:
\[ \text{Total Efficiency} = A + B + C = 3C + 2C + C = 6C \]

### Step 3: Work Done Together
According to the problem, working together they can complete the work in 10 days. Therefore, their combined work rate is:
\[ \text{Work Rate} = \frac{1 \text{ work}}{10 \text{ days}} = \frac{1}{10} \]

Since their total efficiency is \( 6C \), we can equate this to their work rate:
\[ 6C = \frac{1}{10} \]

### Step 4: Find Chandu's Efficiency
To find \( C \):
\[ C = \frac{1}{10 \times 6} = \frac{1}{60} \]

### Step 5: Calculate Individual Efficiencies
Now we can find the efficiencies of Bharath and Anand:
- Chandu's efficiency \( C = \frac{1}{60} \)
- Bharath's efficiency \( B = 2C = 2 \times \frac{1}{60} = \frac{1}{30} \)
- Anand's efficiency \( A = 3C = 3 \times \frac{1}{60} = \frac{1}{20} \)

### Step 6: Calculate Days for Anand to Complete the Work Alone
To find out how many days Anand would take to complete the work alone, we use the formula:
\[ \text{Days} = \frac{1 \text{ work}}{\text{Efficiency of Anand}} = \frac{1}{\frac{1}{20}} = 20 \text{ days} \]

### Final Answer
Anand alone can complete the work in **20 days**.

---