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It seems like I am having troubles while dealing with dishonest merchants! Here is another problem:

A cloth merchant says that due to slump in the market, he sells the cloth at $10\%$ loss but he uses a false meter scale and actually gains $15\%$.Find the actual length of the scale.

Any hints, solution, explanation are welcome.

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You might try to find an honest merchant – Ross Millikan Jan 2 '11 at 12:14

So he sells the cloth at 0.9 of "value". What is the 15% taken on? If 15% of the selling price is profit, then he bought at 0.85*0.9. If 15% of his purchase price is his profit, let the buy price be b. 0.9=1.15b, so b=0.9/1.15 These are very close when the profit is small compared to 1, but try it at 40% and see what happens.

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No upvote because you tell him the final result. This is probably homework and should teach something. – FUZxxl Jan 2 '11 at 11:51
@FUZxxl:This is not my homework. – Quixotic Jan 2 '11 at 11:59

I think the question itself is a bit unclear, I interpret it like this:

  • He buys clothes for $n\frac\$m$ (units are set by me), but he sells for $0.9n\frac\$m$
  • But because his scale is too short, the actually price paid by his customers is $1.15n\frac\$m$.

Thus, if the scale's length is just $xm$ instead of one meter, the equation is like this:

$$0.9n\frac\$m = 1.15n\frac\${xm}$$

Try to figure out the solution by your self and see whether it holds.

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