Shantanu can do a piece of work in 12 days and Manu can do the same work in 10 days. If they work together, in what ratio Shantanu and Manu will receive their wages?

Options

A. `5:6`
B. `3:2`
C. `1:6`
D. `5:7`

Answer

To solve the problem of determining the ratio in which Shantanu and Manu will receive their wages when they work together, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Work Done by Each Person in One Day**:
- Shantanu can complete the work in 12 days. Therefore, his work done in one day is:
\[ \text{Work done by Shantanu in one day} = \frac{1}{12} \]
- Manu can complete the work in 10 days. Therefore, his work done in one day is:
\[ \text{Work done by Manu in one day} = \frac{1}{10} \]

2. **Find a Common Denominator**:
- To compare their work rates easily, we can find a common denominator for their work rates. The least common multiple (LCM) of 12 and 10 is 60.

3. **Calculate the Work Done in Terms of the LCM**:
- Convert their work rates to a common base:
- Shantanu's work in terms of the LCM:
\[ \text{Work done by Shantanu} = \frac{60}{12} = 5 \text{ units of work} \]
- Manu's work in terms of the LCM:
\[ \text{Work done by Manu} = \frac{60}{10} = 6 \text{ units of work} \]

4. **Calculate the Total Work Done Together**:
- When they work together, the total work done in one day is:
\[ \text{Total work done} = 5 + 6 = 11 \text{ units of work} \]

5. **Determine the Ratio of Their Work**:
- The ratio of work done by Shantanu to the work done by Manu is:
\[ \text{Ratio} = \frac{\text{Work done by Shantanu}}{\text{Work done by Manu}} = \frac{5}{6} \]

6. **Conclusion**:
- Therefore, the ratio in which Shantanu and Manu will receive their wages is:
\[ \text{Ratio of wages} = 5:6 \]

### Final Answer:
Shantanu and Manu will receive their wages in the ratio of **5:6**.

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