Question : Ritika purchased 'x' kg wheat at Rs. 30/kg and sold 8 kg of this at Rs. 'x' per kg and remaining at Rs. 45/kg. The overall profit percentage earned is 10%, then what quantity of wheat does Ritika sell at Rs. 45/kg?
Option 1: 18 kg
Option 2: 16 kg
Option 3: 10 kg
Option 4: 14 kg
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Correct Answer: 10 kg
Solution :
Given:
Cost price of wheat = Rs. 30 per kg
Selling price of 8 kg = Rs. $x$ per kg
The selling price of the remaining wheat = Rs. 45 per kg
Overall profit percentage = 10%
Total cost price = CP = Rs. $30 \times x = 30x$
Profit must be 10%
So, SP = $30x \times \frac{110}{100} = 33x$
For the first 8 kg of wheat, the selling price is Rs. $x$ per kg.
Selling price of 8 kg = $8 \times x = 8x$
For the remaining wheat, the selling price is Rs. 45 per kg.
Remaining quantity = $(x - 8)$ kg
According to the question
⇒ $33x = 8x + (x - 8)45$
⇒ $33x = 8x + 45x - 8 \times 45$
⇒ $x = 18$ kg
Quantity of wheat sold at Rs. 45 per kg = $(x - 8) = 18 - 8 = 10$ kg
Therefore, Ritika sold 10 kg of wheat at Rs. 45 per kg.
Hence, the correct answer is 10 kg.
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