1250 Persons went to see a circus-show. Each adult paid `75rs` and each child paid `25rs` for the admission ticket. Find the number of adults and number of children, if the total collection from them amounts to `61250rs`.

Answer

To solve the problem of finding the number of adults and children who attended the circus show, we can set up a system of equations based on the information provided.

### Step 1: Define Variables
Let:
- \( x \) = number of adults
- \( y \) = number of children

### Step 2: Set Up the Equations
From the problem, we have two key pieces of information:
1. The total number of persons (adults + children) is 1250.
2. The total collection from ticket sales is 61250 Rs.

From this, we can create the following equations:
1. \( x + y = 1250 \) (Equation 1)
2. \( 75x + 25y = 61250 \) (Equation 2)

### Step 3: Simplify Equation 2
To make calculations easier, we can simplify Equation 2. We can divide the entire equation by 25:
\[ 3x + y = 2450 \quad \text{(Equation 3)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
1. \( x + y = 1250 \) (Equation 1)
2. \( 3x + y = 2450 \) (Equation 3)

We can subtract Equation 1 from Equation 3:
\[ (3x + y) - (x + y) = 2450 - 1250 \]
This simplifies to:
\[ 2x = 1200 \]
Dividing both sides by 2 gives:
\[ x = 600 \]

### Step 5: Find the Number of Children
Now that we have the number of adults, we can find the number of children using Equation 1:
\[ y = 1250 - x = 1250 - 600 = 650 \]

### Conclusion
Thus, the number of adults is 600 and the number of children is 650.

### Final Answer:
- Number of Adults: 600
- Number of Children: 650