Some fruits are bought at a rate of 11 for 100 rupees and an equal number at a rate of 9 for 100 rupees. If all the fruits are sold at a rate of 10 for 100 rupees, then what is the gain or loss percent in the entire transaction?
Question
Some fruits are bought at a rate of 11 for 100 rupees and an equal number at a rate of 9 for 100 rupees. If all the fruits are sold at a rate of 10 for 100 rupees, then what is the gain or loss percent in the entire transaction?
Solution
Sure, let's break this down:
Step 1: Determine the cost price of the fruits
The cost price of 11 fruits is 100 rupees, so the cost price of 1 fruit is 100/11 = 9.09 rupees.
The cost price of 9 fruits is also 100 rupees, so the cost price of 1 fruit is 100/9 = 11.11 rupees.
Step 2: Determine the selling price of the fruits
The fruits are sold at a rate of 10 for 100 rupees, so the selling price of 1 fruit is 100/10 = 10 rupees.
Step 3: Determine the gain or loss percent
The cost price of 1 fruit bought at 11 for 100 rupees and 1 fruit bought at 9 for 100 rupees is 9.09 + 11.11 = 20.20 rupees.
The selling price of 2 fruits is 2 * 10 = 20 rupees.
So, there is a loss in the transaction. The loss percent can be calculated as:
Loss % = [(Cost Price - Selling Price) / Cost Price] * 100 = [(20.20 - 20) / 20.20] * 100 = [0.20 / 20.20] * 100 = 0.99 %
So, there is a loss of approximately 0.99% in the entire transaction.
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