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 the variables, set up equations based on the information provided, and then solve for the unknowns.

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

### Step 2: Set Up Equations
From the problem, we know:
1. The total cost of post cards and inland letters is Rs. 33.
- The cost of one post card = 15 paise = Rs. 0.15
- The cost of one inland letter = 75 paise = Rs. 0.75
- Therefore, the equation for total cost is:
\[ 0.15x + 0.75y = 33 \]

2. The total number of post cards and inland letters purchased is 60.
- Therefore, the equation for total quantity is:
\[ x + y = 60 \]

### Step 3: Simplify the Equations
We can simplify the first equation by multiplying everything by 100 to eliminate decimals:
\[ 15x + 75y = 3300 \]

Now we have the system of equations:
1. \( 15x + 75y = 3300 \) (Equation 1)
2. \( x + y = 60 \) (Equation 2)

### Step 4: Solve the System of Equations
From Equation 2, we can express \( y \) in terms of \( x \):
\[ y = 60 - x \]

Now substitute \( y \) in Equation 1:
\[ 15x + 75(60 - x) = 3300 \]
Expanding this gives:
\[ 15x + 4500 - 75x = 3300 \]
Combine like terms:
\[ -60x + 4500 = 3300 \]
Subtract 4500 from both sides:
\[ -60x = 3300 - 4500 \]
\[ -60x = -1200 \]
Now divide by -60:
\[ x = 20 \]

### Step 5: Find \( y \)
Now substitute \( x = 20 \) back into Equation 2:
\[ 20 + y = 60 \]
\[ y = 60 - 20 = 40 \]

### Step 6: Interchange the Numbers
Now, if the number of post cards and inland letters are interchanged:
- New number of post cards = \( y = 40 \)
- New number of inland letters = \( x = 20 \)

### Step 7: Calculate the New Cost
1. Cost of 40 post cards:
\[ \text{Cost of post cards} = 0.15 \times 40 = 6 \text{ Rs.} \]

2. Cost of 20 inland letters:
\[ \text{Cost of inland letters} = 0.75 \times 20 = 15 \text{ Rs.} \]

### Step 8: Total Cost
Total cost when the numbers are interchanged:
\[ \text{Total Cost} = 6 + 15 = 21 \text{ Rs.} \]

### Final Answer
The total cost when the number of post cards and inland letters are interchanged is **Rs. 21**.

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