A fruit seller buys some oranges at the rate of 4 for Rs 10 and an equal number more at 5 for 10. He sells the whole lot at 9 for Rs 20. What is his loss or gain per cent ?

Options

A. Loss per cent `1 19/81 %`
B. Gain precent `1 19/81%`
C. No loss or no profit
D. Loss per cent 2%

Answer

To solve the problem step by step, we will calculate the cost price (CP), selling price (SP), and then determine the loss or gain percentage.

### Step 1: Calculate the Cost Price (CP)

1. **Buying the first batch of oranges:**
- The seller buys oranges at the rate of 4 for Rs. 10.
- Let’s say he buys 20 oranges.
- The cost for 20 oranges = (20/4) * 10 = 5 * 10 = Rs. 50.

2. **Buying the second batch of oranges:**
- The seller buys oranges at the rate of 5 for Rs. 10.
- Again, for 20 oranges.
- The cost for 20 oranges = (20/5) * 10 = 4 * 10 = Rs. 40.

3. **Total Cost Price (CP):**
- Total CP = Cost of first batch + Cost of second batch = Rs. 50 + Rs. 40 = Rs. 90.

### Step 2: Calculate the Selling Price (SP)

1. **Selling the whole lot:**
- The seller sells the oranges at the rate of 9 for Rs. 20.
- Total number of oranges = 20 (from the first batch) + 20 (from the second batch) = 40 oranges.
- The selling price for 40 oranges = (40/9) * 20 = (40 * 20) / 9 = Rs. 800 / 9.

### Step 3: Calculate Loss or Gain

1. **Determine the loss:**
- CP = Rs. 90
- SP = Rs. 800 / 9
- To find the loss, we first need to express CP and SP in a comparable form.
- Convert CP into a fraction: CP = 90 = 810 / 9 (to have a common denominator).

2. **Calculate the loss:**
- Loss = CP - SP = (810/9) - (800/9) = (810 - 800) / 9 = 10 / 9.

### Step 4: Calculate Loss Percentage

1. **Loss Percentage Formula:**
- Loss Percentage = (Loss / CP) * 100
- Loss Percentage = [(10/9) / 90] * 100 = (10 / 9 * 1/90) * 100 = (10 / 810) * 100 = 1000 / 81.

2. **Final Calculation:**
- Loss Percentage = 100 / 81.

### Conclusion

The loss percentage is approximately 1.23% (or 100/81%).