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 July 29th, 2019, 07:21 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 458 Thanks: 1 Is this sentence necessary in the question? One trader calculates the percentage of profit on the buying price and another calculates on the S.P. When their selling prices are the same, then the difference of their actual profits is Rs 85 and both claim to have made 20% profit. What is the selling price of each? Is this sentence necessary in the question?
 July 29th, 2019, 08:23 AM #2 Senior Member   Joined: Jun 2019 From: USA Posts: 120 Thanks: 40 Yes, it tells you which equation each person is using to calculate "profit." For Ajay (or trader 1): P1 = 0.2 * BP1 For Bibin (or trader 2): P2 = 0.2 * SP2 The statement claims that SP1 = SP2, and that either P2 - P1 = Rs 85 or P1 - P2 = Rs 85. For simplicity, we can call the selling price SP1 = SP2 = SP. What is profit? Net money earned, right? So P = SP - BP. --> SP - BP1 = 0.2 * BP1 (1) SP - BP2 = 0.2 * SP (2) SP must be greater than BP1 (they made a positive profit), so P2 must be bigger than P1 --> P2 - P1 = (SP - BP2) - (SP - BP1) = Rs 85 (3a) The SP values cancel out. --> BP1 - BP2 = Rs 85 (3b) (1) --> SP = 1 * BP1 + 0.2 * BP1 = 1.2 * BP1 (1b) (2) --> 1 * SP - 0.2 * SP = (1 - 0.2) * SP = 0.8 * SP = BP2 (2b) Rearrange (1b) --> BP1 = SP / (1.2) = (5/6) * SP (1c) Substitute (1c) and (2b) into (3b) --> (5/6) * SP - (4/5) * SP = Rs 85 $\displaystyle \rightarrow (\frac{5}{6} - \frac{4}{5})*SP = Rs~ 85$ Hopefully you can calculate it from there, yes?

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