Anil, Bhuvan and Chirag together can complete a work in 35 days. Anil and Chirag together can complete the same work in 60 days. In how many days Bhuvan alone can complete the same work?

Options

A. 105 days
B. 84 days
C. 96 days
D. 110 days

Answer

To solve the problem step by step, we will denote the work done by Anil, Bhuvan, and Chirag as A, B, and C respectively.

### Step 1: Determine the combined work rate of Anil, Bhuvan, and Chirag
Given that Anil, Bhuvan, and Chirag together can complete the work in 35 days, their combined work rate is:
\[ \text{Work rate of (A + B + C)} = \frac{1}{35} \text{ (work per day)} \]

### Step 2: Determine the combined work rate of Anil and Chirag
We are also given that Anil and Chirag together can complete the work in 60 days, so their combined work rate is:
\[ \text{Work rate of (A + C)} = \frac{1}{60} \text{ (work per day)} \]

### Step 3: Find Bhuvan's work rate
To find Bhuvan's work rate (B), we can use the work rates we found in Steps 1 and 2. We know:
\[ \text{Work rate of (A + B + C)} - \text{Work rate of (A + C)} = \text{Work rate of B} \]
Substituting the values we have:
\[ \frac{1}{35} - \frac{1}{60} = B \]

### Step 4: Calculate the left-hand side (LCM)
To perform the subtraction, we need to find the least common multiple (LCM) of 35 and 60. The LCM of 35 and 60 is 420. Now we can rewrite the fractions:
\[ \frac{1}{35} = \frac{12}{420}, \quad \frac{1}{60} = \frac{7}{420} \]
Now, substituting these into the equation:
\[ B = \frac{12}{420} - \frac{7}{420} = \frac{5}{420} \]

### Step 5: Simplify Bhuvan's work rate
Now, simplifying \(\frac{5}{420}\):
\[ B = \frac{1}{84} \]
This means Bhuvan can complete \(\frac{1}{84}\) of the work in one day.

### Step 6: Calculate the number of days Bhuvan takes to complete the work alone
If Bhuvan can complete \(\frac{1}{84}\) of the work in one day, then the total number of days Bhuvan will take to complete the work alone is:
\[ \text{Days} = \frac{1}{\frac{1}{84}} = 84 \text{ days} \]

### Final Answer
Thus, Bhuvan alone can complete the work in **84 days**.

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