Post cards costing 15 paise each and inland letters costing 75 paise each were purchased for Rs. 33. Total number of post cards and inland letters purchased was 60. If the number of post cards and inland letters are interchanged, find the cost.

Answer

To solve the problem step by step, we will define variables, set up equations based on the information provided, and then solve those equations.

### Step 1: Define Variables
Let:
- \( x \) = number of post cards
- \( y \) = number of inland letters

### Step 2: Set Up the Equations
From the problem, we have two pieces of information:
1. The total number of post cards and inland letters is 60.
2. The total cost of the post cards and inland letters is Rs. 33.

We can express these as equations:
1. \( x + y = 60 \) (Equation 1)
2. The cost of post cards is \( 15 \) paise each, and the cost of inland letters is \( 75 \) paise each. Therefore, the total cost can be expressed as:
\[ 15x + 75y = 3300 \quad \text{(since Rs. 33 = 3300 paise)} \]
(Equation 2)

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing all terms by 15:
\[ x + 5y = 220 \quad \text{(Equation 2 simplified)} \]

### Step 4: Solve the System of Equations
Now we have the system of equations:
1. \( x + y = 60 \) (Equation 1)
2. \( x + 5y = 220 \) (Equation 2)

We can solve these equations simultaneously.

From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = 60 - y \]

Now, substitute \( x \) in Equation 2:
\[ (60 - y) + 5y = 220 \]
\[ 60 + 4y = 220 \]
\[ 4y = 220 - 60 \]
\[ 4y = 160 \]
\[ y = 40 \]

Now substitute \( y \) back into Equation 1 to find \( x \):
\[ x + 40 = 60 \]
\[ x = 60 - 40 \]
\[ x = 20 \]

### Step 5: Conclusion
Thus, the number of post cards is \( 20 \) and the number of inland letters is \( 40 \).

### Step 6: Calculate the Cost
Now, we need to find the total cost when the number of post cards and inland letters are interchanged. This means:
- Number of post cards = 40
- Number of inland letters = 20

Now, calculate the cost:
\[ \text{Cost of post cards} = 40 \times 15 \text{ paise} = 600 \text{ paise} \]
\[ \text{Cost of inland letters} = 20 \times 75 \text{ paise} = 1500 \text{ paise} \]

Total cost:
\[ 600 + 1500 = 2100 \text{ paise} = 21 \text{ Rs.} \]

### Final Answer
The total cost after interchanging the number of post cards and inland letters is Rs. 21.