A box contains one rupee, fifty-paise and twenty-five paise coins. The total number of coins is 378. The ratio of values of the above coins is `13 : 11:7`. The number of twenty-five palse coins is :

Options

A. 168
B. 210
C. 132
D. 78

Answer

To solve the problem step by step, we will follow the guidelines provided in the video transcript.

### Step-by-Step Solution:

1. **Understanding the Coin Values**:
- The values of the coins are:
- 1 Rupee = 100 Paise
- 50 Paise = 50 Paise
- 25 Paise = 25 Paise

2. **Setting Up the Ratios**:
- The ratio of the values of the coins is given as 13:11:7.
- This means:
- Value of 1 Rupee coins = 13 parts
- Value of 50 Paise coins = 11 parts
- Value of 25 Paise coins = 7 parts

3. **Calculating the Total Value**:
- Total value in terms of Paise:
- Value of 1 Rupee coins = 13 * 100 = 1300 Paise
- Value of 50 Paise coins = 11 * 50 = 550 Paise
- Value of 25 Paise coins = 7 * 25 = 175 Paise
- Total value = 1300 + 550 + 175 = 2025 Paise

4. **Finding the Number of Coins**:
- Let the number of 1 Rupee coins be \( x \), 50 Paise coins be \( y \), and 25 Paise coins be \( z \).
- The values can be expressed in terms of the number of coins:
- \( 100x = 13k \) (for 1 Rupee coins)
- \( 50y = 11k \) (for 50 Paise coins)
- \( 25z = 7k \) (for 25 Paise coins)
- Where \( k \) is a common factor.

5. **Expressing the Number of Coins**:
- From the equations:
- \( x = \frac{13k}{100} \)
- \( y = \frac{11k}{50} \)
- \( z = \frac{7k}{25} \)

6. **Finding the Total Number of Coins**:
- The total number of coins is given as 378:
\[ x + y + z = 378 \]
- Substitute the expressions for \( x, y, z \):
\[ \frac{13k}{100} + \frac{11k}{50} + \frac{7k}{25} = 378 \]

7. **Finding a Common Denominator**:
- The common denominator for 100, 50, and 25 is 100.
- Rewrite the equation:
\[ \frac{13k}{100} + \frac{22k}{100} + \frac{28k}{100} = 378 \]
- Combine the fractions:
\[ \frac{63k}{100} = 378 \]

8. **Solving for \( k \)**:
- Multiply both sides by 100:
\[ 63k = 37800 \]
- Divide by 63:
\[ k = \frac{37800}{63} = 600 \]

9. **Finding the Number of 25 Paise Coins**:
- Substitute \( k \) back into the expression for \( z \):
\[ z = \frac{7k}{25} = \frac{7 \times 600}{25} = \frac{4200}{25} = 168 \]

### Final Answer:
The number of twenty-five paise coins is **168**.