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
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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