Question : The selling prices of articles A and B are the same. A is sold at a profit of 28% and B is sold at a loss of 24%. If the total selling price of both articles is INR 48640, then what is the cost price of A and B, respectively?
Option 1: INR 26000 and INR 40000
Option 2: INR 24000 and INR 38000
Option 3: INR 17000 and INR 28000
Option 4: INR 19000 and INR 32000
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Correct Answer: INR 19000 and INR 32000
Solution : Given: The selling prices of articles A and B are the same. A is sold at a profit of 28% and B is sold at a loss of 24%. According to the question, 2 SP = INR 48640 ⇒ SP = INR 24320 Use the formulas, Profit = SP – CP Loss = CP – SP Loss percentage = $\frac{\text{Loss}}{CP}\times 100$ Profit percentage = $\frac{\text{Profit}}{CP}\times 100$ Where SP = selling price and CP = cost price. For the article A, Profit = 24320 – CP ⇒ 28 = $\frac{24320–CP}{CP}\times 100$ ⇒ 0.28 CP = 24320 – CP ⇒ 1.28 CP = 24320 ⇒ CP = INR 19000 For the article B, Loss = CP – 24320 ⇒ 24 = $\frac{CP–24320}{CP}\times 100$ ⇒ 0.24 CP = CP – 24320 ⇒ 0.76 CP = 24320 ⇒ CP = INR 32000 Hence, the correct answer is INR 19000 and INR 32000.
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