Hari purchased 25 kg of wheat at the rate of ₹4 per kg and 35 kg of wheat at ₹4.50 per kg. He sold the mixture

Question

Hari purchased 25 kg of wheat at the rate of ₹4 per kg and 35 kg of wheat at ₹4.50 per kg. He sold the mixture at the rate of ₹4.25 per kg. Find his gain or loss.

Examoogle · Accepted Answer

The correct answer is Option C: ₹2.50, loss. Calculate the difference from the base price of 4 for the second quantity: 35 kg is 0.50 above, so gain 17.5. Weighted average price is 4 + (35 * 0.5) / 60 = 4 + 17.5/60 ≈ 4.29. Since selling price 4.25 < 4.29, it is a loss.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate the difference from the base price of 4 for the second quantity: 35 kg is 0.50 above, so gain 17.5. Weighted average price is 4 + (35 * 0.5) / 60 = 4 + 17.5/60 ≈ 4.29. Since selling price 4.25

Formula Used: $$Cost \ Price = (Q_1 	imes R_1) + (Q_2 	imes R_2)$$, $$Total \ Quantity = Q_1 + Q_2$$, $$Selling \ Price = Total \ Quantity 	imes R_{sale}$$, $$Profit/Loss = SP - CP$$

Given: Quantity 1: 25 kg at ₹4/kg. Quantity 2: 35 kg at ₹4.50/kg. Selling Price: ₹4.25/kg.

Steps: Calculate Total Cost Price: Find the total investment for both quantities: $25 	imes 4 + 35 	imes 4.50 = 100 + 157.50$.. Calculate Total Selling Price: Total weight is $25 + 35 = 60$ kg, sold at $4.25$ per kg: $60 	imes 4.25$.. Determine Profit or Loss: Since $CP > SP$, it is a loss: $257.50 - 255.00$.

Answer: C is correct because the total cost price is ₹257.50 and the total selling price is ₹255.00, resulting in a loss of ₹2.50.

Exam Tip: Always use the weighted average formula $Avg = \frac{n_1 x_1 + n_2 x_2}{n_1 + n_2}$ for mixture problems to avoid common arithmetic errors.

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