A certain amount of money Is divided among x, y and z. If x receives 25% more than y and y receives 25% less than z, then `x: y : z` Is equal to

Options

A. `14 : 12 : 13`
B. `15 : 12 : 16`
C. `10 : 9 : 12`
D. `12 : 10 : 11`

Answer

To solve the problem of dividing a certain amount of money among x, y, and z based on the given conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationships**:
- We know that x receives 25% more than y.
- We also know that y receives 25% less than z.

2. **Assigning Variables**:
- Let the amount that y receives be denoted as \( y \).
- Since x receives 25% more than y, we can express x as:
\[ x = y + 0.25y = 1.25y \]

3. **Expressing y in terms of z**:
- Since y receives 25% less than z, we can express y in terms of z:
\[ y = z - 0.25z = 0.75z \]

4. **Substituting y in the equation for x**:
- Now, substitute \( y = 0.75z \) into the equation for x:
\[ x = 1.25y = 1.25(0.75z) = 0.9375z \]

5. **Finding the ratio x : y : z**:
- Now we have:
- \( x = 0.9375z \)
- \( y = 0.75z \)
- \( z = z \)
- To find the ratio, we can express all amounts in terms of z:
\[ x : y : z = 0.9375z : 0.75z : z \]
- Dividing each term by z (assuming z ≠ 0):
\[ x : y : z = 0.9375 : 0.75 : 1 \]

6. **Converting to a simpler form**:
- To eliminate decimals, we can multiply each term by 16 (the least common multiple of the denominators):
\[ 0.9375 \times 16 : 0.75 \times 16 : 1 \times 16 = 15 : 12 : 16 \]

7. **Final Ratio**:
- Therefore, the final ratio \( x : y : z \) is:
\[ \boxed{15 : 12 : 16} \]