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If the rice is sold at Rs 56 per kg, the...

If the rice is sold at Rs 56 per kg, there would be at 40% loss. To earn a profit of 20% what should be the price of rice (per kg)?

A

112

B

108

C

116

D

124

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, let's first define the variables and understand the relationships between cost price (CP), selling price (SP), profit, and loss. ### Step 1: Define the Cost Price (CP) Let the cost price of rice be \( CP \) rupees per kg. ### Step 2: Understand the Loss Condition According to the problem, if the rice is sold at Rs 56 per kg, there is a loss of 40%. This means that selling price (SP) is 60% of the cost price (CP). \[ SP = CP - \text{Loss} = CP \times (1 - \text{Loss Percentage}) \] Given that the loss percentage is 40%, we can express this as: \[ SP = CP \times (1 - 0.40) = CP \times 0.60 \] ### Step 3: Set Up the Equation We know the selling price (SP) when there is a loss is Rs 56. Therefore, we can set up the equation: \[ 56 = CP \times 0.60 \] ### Step 4: Solve for CP To find the cost price (CP), we rearrange the equation: \[ CP = \frac{56}{0.60} \] Calculating this gives: \[ CP = \frac{56}{0.60} = \frac{56 \times 100}{60} = \frac{5600}{60} = 93.33 \text{ rupees (approximately)} \] ### Step 5: Determine the New Selling Price for Profit Now, we want to find the selling price that would yield a profit of 20%. The selling price for a profit can be calculated as: \[ SP = CP \times (1 + \text{Profit Percentage}) \] Given that the profit percentage is 20%, we can express this as: \[ SP = CP \times (1 + 0.20) = CP \times 1.20 \] ### Step 6: Substitute CP into the Profit Equation Substituting the value of \( CP \) we found earlier: \[ SP = 93.33 \times 1.20 \] Calculating this gives: \[ SP = 112 \text{ rupees} \] ### Final Answer Thus, to earn a profit of 20%, the price of rice should be sold at Rs 112 per kg. ---
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