615coins include one rupees, 50paise and 25paise coins. There values are in the ratio 3:5:7 respectively. Find the number of 50paise coins

To solve this problem, let's break it down step by step.

### Step 1: Define the Variables
Let:
- \( x \) be the total value of 1 rupee coins.
- \( y \) be the total value of 50 paise coins.
- \( z \) be the total value of 25 paise coins.

Given that the values are in the ratio \( 3:5:7 \), we can express these as:
- \( x = 3k \)
- \( y = 5k \)
- \( z = 7k \)

Where \( k \) is a constant.

### Step 2: Calculate the Number of Coins
Next, we convert these values into the number of coins.

- For 1 rupee coins (100 paise): \( \text{Number of 1 rupee coins} = \frac{x}{100} = \frac{3k}{100} \)
- For 50 paise coins: \( \text{Number of 50 paise coins} = \frac{y}{50} = \frac{5k}{50} = \frac{k}{10} \)
- For 25 paise coins: \( \text{Number of 25 paise coins} = \frac{z}{25} = \frac{7k}{25} = \frac{7k}{25} \)

### Step 3: Total Number of Coins
According to the problem, the total number of coins is 615. So, we can write the equation as:

\[
\frac{3k}{100} + \frac{k}{10} + \frac{7k}{25} = 615
\]

### Step 4: Simplify and Solve for \( k \)
First, find a common denominator for the fractions:

\[
\frac{3k}{100} + \frac{k}{10} + \frac{7k}{25} = \frac{3k}{100} + \frac{10k}{100} + \frac{28k}{100} = \frac{41k}{100}
\]

So, the equation becomes:

\[
\frac{41k}{100} = 615
\]

Now, solve for \( k \):

\[
41k = 61500
\]

\[
k = \frac{61500}{41} = 1500
\]

### Step 5: Find the Number of 50 Paise Coins
The number of 50 paise coins is \( \frac{k}{10} \):

\[
\text{Number of 50 paise coins} = \frac{1500}{10} = 150
\]

### Final Answer
The number of 50 paise coins is **150**.

Would you like more details or have any questions?

Here are five related questions:
1. How many 25 paise coins are there?
2. How would the answer change if the total number of coins was different?
3. What is the total value of all the coins combined?
4. How many 1 rupee coins are there?
5. How can ratios help in solving similar coin problems?

**Tip:** When dealing with coins and ratios, always convert the values to the smallest unit (like paise) for easier calculations.

Learn how to solve a ratio problem involving 1 rupee, 50 paise, and 25 paise coins. Discover step-by-step how to find the number of 50 paise coins given the ratio of 3:5:7 and a total of 615 coins. Suitable for Grades 7-9.

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