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July 29th, 2019, 07:21 AM   #1
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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?
Ganesh Ujwal is offline  
 
July 29th, 2019, 08:23 AM   #2
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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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