One day in summer I wanted to chill me out, I went to a cool corner. I gave him a note of ₹ 10 and asked for a coke costing ₹ 5 per jar and he did so, but he returned me ₹ 5, in the denomination of ₹ 1, 50 paise and 25 paise. What could be the ratio of no. of coins of ₹ 1, 50 paise and 25 paise respectively :

Options

A. 1:2:3
B. 1:1:3
C. 2:3:4
D. 1:2:2

Answer

To solve the problem of finding the ratio of the number of coins of ₹1, 50 paise, and 25 paise that sum up to ₹5, we can follow these steps:

### Step 1: Define the variables
Let:
- \( x \) = number of ₹1 coins
- \( y \) = number of 50 paise coins
- \( z \) = number of 25 paise coins

### Step 2: Set up the equation for the total amount
The total amount returned is ₹5. We can express this in terms of the coins:
\[ x \cdot 1 + y \cdot 0.50 + z \cdot 0.25 = 5 \]

### Step 3: Convert all amounts to the same unit
To make calculations easier, we can convert everything to paise (1 rupee = 100 paise):
\[ x \cdot 100 + y \cdot 50 + z \cdot 25 = 500 \]

### Step 4: Simplify the equation
Now, we can simplify the equation:
\[ 100x + 50y + 25z = 500 \]
Dividing the entire equation by 25 gives:
\[ 4x + 2y + z = 20 \]

### Step 5: Find possible integer solutions
Now we need to find integer solutions for \( x \), \( y \), and \( z \) that satisfy this equation. We can try different values for \( x \) and solve for \( y \) and \( z \).

1. **Assume \( x = 1 \)**:
\[ 4(1) + 2y + z = 20 \implies 2y + z = 16 \]

2. **Assume \( x = 2 \)**:
\[ 4(2) + 2y + z = 20 \implies 2y + z = 12 \]

3. **Assume \( x = 3 \)**:
\[ 4(3) + 2y + z = 20 \implies 2y + z = 8 \]

4. **Assume \( x = 4 \)**:
\[ 4(4) + 2y + z = 20 \implies 2y + z = 4 \]

5. **Assume \( x = 5 \)**:
\[ 4(5) + 2y + z = 20 \implies 2y + z = 0 \]

### Step 6: Find integer combinations
From the above equations, we can find combinations of \( y \) and \( z \):

- For \( x = 1 \): \( 2y + z = 16 \) (e.g., \( y = 8, z = 0 \))
- For \( x = 2 \): \( 2y + z = 12 \) (e.g., \( y = 6, z = 0 \))
- For \( x = 3 \): \( 2y + z = 8 \) (e.g., \( y = 4, z = 0 \))
- For \( x = 4 \): \( 2y + z = 4 \) (e.g., \( y = 2, z = 0 \))
- For \( x = 5 \): \( 2y + z = 0 \) (e.g., \( y = 0, z = 0 \))

### Step 7: Calculate the ratio
Assuming \( x = 4 \), \( y = 2 \), and \( z = 0 \):
- The ratio of coins is \( x:y:z = 4:2:0 \).
- Simplifying this gives us \( 4:2:0 \) or \( 2:1:0 \).

### Final Answer
The ratio of the number of coins of ₹1, 50 paise, and 25 paise is **2:1:0**.