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In my pocket there are rs 25 consisting ...

In my pocket there are rs 25 consisting of only the denominations of 20 paise and 50 paise. Thus there are total 80 coins in my pocket. The no. of coins of the denomination of 50 paise is:

A

30

B

70

C

50

D

25

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The correct Answer is:
To solve the problem, we need to find the number of coins of 50 paise in a total of 80 coins, which consist of only 20 paise and 50 paise coins that add up to Rs. 25. ### Step-by-Step Solution: 1. **Define Variables**: Let: - \( x \) = number of 20 paise coins - \( y \) = number of 50 paise coins 2. **Set Up Equations**: We have two equations based on the information given: - The total number of coins: \[ x + y = 80 \quad \text{(1)} \] - The total value of the coins in rupees: \[ 0.20x + 0.50y = 25 \quad \text{(2)} \] 3. **Convert Equation (2)**: To eliminate decimals, multiply the entire equation by 100: \[ 20x + 50y = 2500 \quad \text{(3)} \] 4. **Solve for One Variable**: From equation (1), we can express \( x \) in terms of \( y \): \[ x = 80 - y \quad \text{(4)} \] 5. **Substitute into Equation (3)**: Substitute equation (4) into equation (3): \[ 20(80 - y) + 50y = 2500 \] Simplifying this gives: \[ 1600 - 20y + 50y = 2500 \] \[ 30y = 2500 - 1600 \] \[ 30y = 900 \] \[ y = \frac{900}{30} = 30 \] 6. **Find the Number of 20 Paise Coins**: Now substitute \( y \) back into equation (4) to find \( x \): \[ x = 80 - 30 = 50 \] 7. **Conclusion**: The number of coins of the denomination of 50 paise is \( y = 30 \). ### Final Answer: The number of coins of the denomination of 50 paise is **30**.
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