Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages.

Options

A. Rs 40, Rs 60 and Rs 260
B. Rs 36, Rs 81 and Rs 243
C. Rs 42, Rs 86 and Rs 232
D. Rs 38, Rs 88 and Rs 234

Answer

To solve the problem, we need to determine how much work each person (Anil, Bittu, and Chintu) does in a day, find out the total work done over a period of time, and then calculate their respective wages based on the work done.

### Step-by-Step Solution:

1. **Determine the Work Rate of Each Person:**
- Anil can complete the work in 90 days, so his work rate is:
\[ \text{Work done by Anil in 1 day} = \frac{1}{90} \text{ of the total work} \]
- Bittu can complete the work in 40 days, so his work rate is:
\[ \text{Work done by Bittu in 1 day} = \frac{1}{40} \text{ of the total work} \]
- Chintu can complete the work in 12 days, so his work rate is:
\[ \text{Work done by Chintu in 1 day} = \frac{1}{12} \text{ of the total work} \]

2. **Calculate the Total Work in Units:**
- To find a common measure for the work done, we calculate the LCM of the days taken by Anil, Bittu, and Chintu (90, 40, and 12).
- The LCM of 90, 40, and 12 is 360. Thus, the total work can be considered as 360 units.

3. **Calculate the Daily Work Contribution:**
- Now we can convert their daily work rates into units:
- Anil's work per day:
\[ \text{Anil's work} = \frac{360}{90} = 4 \text{ units} \]
- Bittu's work per day:
\[ \text{Bittu's work} = \frac{360}{40} = 9 \text{ units} \]
- Chintu's work per day:
\[ \text{Chintu's work} = \frac{360}{12} = 30 \text{ units} \]

4. **Calculate Total Work Done in a Cycle of 3 Days:**
- In one cycle of 3 days (Anil, Bittu, Chintu), the total work done is:
\[ \text{Total work in 3 days} = 4 + 9 + 30 = 43 \text{ units} \]

5. **Determine How Many Full Cycles Fit into the Total Work:**
- To find out how many complete cycles fit into 360 units:
\[ \text{Number of complete cycles} = \frac{360}{43} \approx 8 \text{ cycles} \]
- Total work done in 8 cycles:
\[ \text{Work done in 24 days} = 8 \times 43 = 344 \text{ units} \]

6. **Calculate Remaining Work:**
- Remaining work after 24 days:
\[ \text{Remaining work} = 360 - 344 = 16 \text{ units} \]

7. **Determine Who Works Next:**
- On the 25th day, Anil works and completes 4 units:
\[ \text{Work done by Anil on 25th day} = 4 \text{ units} \]
- Remaining work after Anil's work:
\[ \text{Remaining work} = 16 - 4 = 12 \text{ units} \]
- On the 26th day, Bittu works and completes 9 units:
\[ \text{Work done by Bittu on 26th day} = 9 \text{ units} \]
- Remaining work after Bittu's work:
\[ \text{Remaining work} = 12 - 9 = 3 \text{ units} \]
- On the 27th day, Chintu works and completes 3 units:
\[ \text{Work done by Chintu on 27th day} = 3 \text{ units} \]

8. **Calculate Total Work Done by Each Person:**
- Total work done by Anil:
\[ \text{Total work by Anil} = 8 \times 4 + 4 = 36 \text{ units} \]
- Total work done by Bittu:
\[ \text{Total work by Bittu} = 8 \times 9 + 9 = 81 \text{ units} \]
- Total work done by Chintu:
\[ \text{Total work by Chintu} = 8 \times 30 + 3 = 243 \text{ units} \]

9. **Calculate Wages Based on Work Done:**
- Total wages = Rs 360
- Wages for Anil:
\[ \text{Wages for Anil} = \frac{36}{360} \times 360 = 36 \text{ Rs} \]
- Wages for Bittu:
\[ \text{Wages for Bittu} = \frac{81}{360} \times 360 = 81 \text{ Rs} \]
- Wages for Chintu:
\[ \text{Wages for Chintu} = \frac{243}{360} \times 360 = 243 \text{ Rs} \]

### Final Wages:
- Anil: Rs 36
- Bittu: Rs 81
- Chintu: Rs 243