A sum of Rs. `125` is divided among u, v and w in such a way that u gets Rs. `10` more than v and v gets Rs.` 5` more than w. What is the ratio of their shares?

Options

A. `12:10:9`
B. `10:8:7`
C. `13:10:7`
D. `5:4:3`

Answer

To solve the problem step by step, let's denote the amounts received by u, v, and w as follows:

1. **Let w = x**: This means that the amount received by w is represented by x.

2. **Determine v**: Since v gets Rs. 5 more than w, we can express v as:
\[ v = x + 5 \]

3. **Determine u**: Since u gets Rs. 10 more than v, we can express u as:
\[ u = v + 10 = (x + 5) + 10 = x + 15 \]

4. **Set up the equation**: The total amount distributed among u, v, and w is Rs. 125. Therefore, we can write the equation:
\[ u + v + w = 125 \]
Substituting the expressions for u, v, and w, we get:
\[ (x + 15) + (x + 5) + x = 125 \]

5. **Combine like terms**: This simplifies to:
\[ 3x + 20 = 125 \]

6. **Solve for x**: To find the value of x, subtract 20 from both sides:
\[ 3x = 125 - 20 \]
\[ 3x = 105 \]
Now, divide by 3:
\[ x = 35 \]

7. **Calculate the shares**:
- For w:
\[ w = x = 35 \]
- For v:
\[ v = x + 5 = 35 + 5 = 40 \]
- For u:
\[ u = x + 15 = 35 + 15 = 50 \]

8. **Write the shares**: Now we have:
- u = 50
- v = 40
- w = 35

9. **Find the ratio of their shares**: The ratio of u, v, and w can be expressed as:
\[ u : v : w = 50 : 40 : 35 \]

10. **Simplify the ratio**: To simplify the ratio, we can divide each term by 5:
\[ 10 : 8 : 7 \]

Thus, the final answer is:
\[ \text{The ratio of their shares is } 10 : 8 : 7. \]