Pankaj purchased 3575 balls and 2002 bats and cost price of one bat is equal to cost price of one ball. He sold ball in such a way that he can buy 850 balls by selling 799 balls and can buy 777 bats by selling 987 bats. Find approximate overall loss/profit percent earned by Pankaj by selling all balls and bats.

Options

A. `4%`
B. `5%`
C. `7%`
D. `6%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price of Balls and Bats
Let the cost price of one ball (CP_ball) be \( x \).
Since the cost price of one bat is equal to the cost price of one ball, we have:
- CP_bat = \( x \)

Now, we can calculate the total cost price (CP) for balls and bats:
- Total CP for balls = Number of balls × CP_ball = \( 3575 \times x \)
- Total CP for bats = Number of bats × CP_bat = \( 2002 \times x \)

Thus, the total cost price (CP_total) is:
\[ CP_{total} = 3575x + 2002x = 5577x \]

### Step 2: Determine the Selling Price Ratio for Balls
According to the problem, selling 799 balls allows Pankaj to buy 850 balls. Therefore, the selling price (SP) of 799 balls can be expressed as:
\[ SP_{799} = CP_{850} \]
This implies:
\[ SP_{799} = 850x \]

Now, we can find the SP to CP ratio for balls:
\[ \frac{SP_{balls}}{CP_{balls}} = \frac{850}{799} \]

### Step 3: Determine the Selling Price Ratio for Bats
Similarly, selling 987 bats allows Pankaj to buy 777 bats. Thus, the selling price of 987 bats can be expressed as:
\[ SP_{987} = CP_{777} \]
This implies:
\[ SP_{987} = 777x \]

Now, we can find the SP to CP ratio for bats:
\[ \frac{SP_{bats}}{CP_{bats}} = \frac{777}{987} \]

### Step 4: Calculate the Net Selling Price and Cost Price
Now we will calculate the total selling price (SP_total) and total cost price (CP_total) using the ratios we found.

1. **Selling Price of Balls:**
- Total SP for balls = Number of balls × SP per ball
- From the ratio, if we let the selling price of one ball be \( \frac{850}{799}x \):
\[ SP_{balls} = 3575 \times \frac{850}{799}x = \frac{3575 \times 850}{799}x \]

2. **Selling Price of Bats:**
- Total SP for bats = Number of bats × SP per bat
- From the ratio, if we let the selling price of one bat be \( \frac{777}{987}x \):
\[ SP_{bats} = 2002 \times \frac{777}{987}x = \frac{2002 \times 777}{987}x \]

### Step 5: Combine Selling Prices
Now we can combine the selling prices:
\[ SP_{total} = SP_{balls} + SP_{bats} = \left(\frac{3575 \times 850}{799} + \frac{2002 \times 777}{987}\right)x \]

### Step 6: Calculate Profit or Loss
To find the profit or loss percentage, we need to calculate:
\[ \text{Profit/Loss} = SP_{total} - CP_{total} \]
Substituting the values:
\[ \text{Profit/Loss} = \left(\frac{3575 \times 850}{799} + \frac{2002 \times 777}{987}\right)x - 5577x \]

### Step 7: Calculate the Profit or Loss Percentage
Finally, the profit or loss percentage can be calculated as:
\[ \text{Profit/Loss Percentage} = \frac{\text{Profit/Loss}}{CP_{total}} \times 100 \]

### Conclusion
After performing the calculations, we find that Pankaj incurred an approximate loss of 4%.