To solve the problem step by step, we need to determine the share of A, B, and C from the total wages of Rs. 535 based on the number of days they take to complete the work individually.
### Step 1: Determine the work done by each person
First, we need to find the amount of work done by A, B, and C in one day.
- A takes 5 days to complete the work, so A's work in one day = \( \frac{1}{5} \)
- B takes 6 days to complete the work, so B's work in one day = \( \frac{1}{6} \)
- C takes 7 days to complete the work, so C's work in one day = \( \frac{1}{7} \)
### Step 2: Calculate the total work done by A, B, and C in one day
Now, we need to find the total work done by A, B, and C together in one day:
\[
\text{Total work in one day} = \frac{1}{5} + \frac{1}{6} + \frac{1}{7}
\]
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 5, 6, and 7 is 210.
Converting each fraction:
- \( \frac{1}{5} = \frac{42}{210} \)
- \( \frac{1}{6} = \frac{35}{210} \)
- \( \frac{1}{7} = \frac{30}{210} \)
Now, adding these fractions:
\[
\text{Total work in one day} = \frac{42 + 35 + 30}{210} = \frac{107}{210}
\]
### Step 3: Calculate the share of each person
The share of each person can be calculated using the formula:
\[
\text{Share of A} = \frac{\text{Total wages} \times \text{Work done by A}}{\text{Total work in one day}}
\]
\[
\text{Share of B} = \frac{\text{Total wages} \times \text{Work done by B}}{\text{Total work in one day}}
\]
\[
\text{Share of C} = \frac{\text{Total wages} \times \text{Work done by C}}{\text{Total work in one day}}
\]
### Step 4: Calculate the individual shares
Now, substituting the values into the formulas:
1. **Share of A**:
\[
\text{Share of A} = \frac{535 \times \frac{1}{5}}{\frac{107}{210}} = \frac{535 \times 42}{107} = 210
\]
2. **Share of B**:
\[
\text{Share of B} = \frac{535 \times \frac{1}{6}}{\frac{107}{210}} = \frac{535 \times 35}{107} = 175
\]
3. **Share of C**:
\[
\text{Share of C} = \frac{535 \times \frac{1}{7}}{\frac{107}{210}} = \frac{535 \times 30}{107} = 150
\]
### Final Shares
- A's share = Rs. 210
- B's share = Rs. 175
- C's share = Rs. 150
