A person can do a piece of work in 26 days and an another person can do the same work in 39 days. If they work together, then by what per cent the wages of 1st person is more than that of 2nd person?

Options

A. `25%`
B. `35%`
C. `15%`
D. `50%`

Answer

To solve the problem step by step, we will determine the efficiencies of both persons and then calculate the percentage difference in their wages based on their efficiencies.

### Step-by-Step Solution:

1. **Identify the Work Rates**:
- Let person A (first person) can complete the work in 26 days.
- Let person B (second person) can complete the work in 39 days.

2. **Calculate the Work Rate of Each Person**:
- Work rate is defined as the fraction of work done in one day.
- For person A:
\[ \text{Work rate of A} = \frac{1}{26} \text{ (work per day)} \]
- For person B:
\[ \text{Work rate of B} = \frac{1}{39} \text{ (work per day)} \]

3. **Find a Common Denominator**:
- The least common multiple (LCM) of 26 and 39 is 78.
- To express their work rates with a common denominator:
- For A:
\[ \text{Work rate of A} = \frac{3}{78} \text{ (since } \frac{1}{26} = \frac{3}{78}\text{)} \]
- For B:
\[ \text{Work rate of B} = \frac{2}{78} \text{ (since } \frac{1}{39} = \frac{2}{78}\text{)} \]

4. **Calculate the Ratio of Their Efficiencies**:
- The ratio of their efficiencies (work rates) is:
\[ \text{Efficiency ratio of A to B} = \frac{3}{2} \]

5. **Determine the Difference in Their Efficiencies**:
- The difference in their efficiencies is:
\[ 3 - 2 = 1 \]

6. **Calculate the Percentage Difference in Wages**:
- To find out how much more the wages of person A are compared to person B, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Difference in efficiency}}{\text{Efficiency of B}} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage} = \left( \frac{1}{2} \right) \times 100 = 50\% \]

### Final Answer:
The wages of the first person (A) are 50% more than the wages of the second person (B).

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