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2015-04-09T09:28:32+05:30

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Let the cost price = x

let the gain when it is sod at Rs 78 is y%.Thus 

 \frac{78-x}{x} \times 100=y\\ \\ \Rightarrow  \frac{100(78-x)}{x}=y\\ \\ \Rightarrow y =  \frac{7800-100x}{x}

When it is sold at Rs. 83, gain is 20% more or gain is (y+20)%.Thus
\frac{83-x}{x} \times 100=y+20\\ \\ \Rightarrow \frac{100(83-x)}{x}=y+20\\ \\ \Rightarrow y+20 = \frac{8300-100x}{x}\\ \\ \Rightarrow \frac{7800-100x}{x}+20 = \frac{8300-100x}{x}\\ \\ \Rightarrow \frac{7800-100x+20x}{x} = \frac{8300-100x}{x}\\ \\ \Rightarrow \frac{7800-80x}{x} = \frac{8300-100x}{x}\\ \\ \Rightarrow 7800-80x= 8300-100x\\ \\ \Rightarrow 100x-80x= 8300-7800\\ \\ \Rightarrow 20x=500\\ \\ \Rightarrow x= \frac{500}{20}=Rs. 25

So the cost price is Rs. 25.

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Alternatively:

Let cost price = x
When the cloth is sold at Rs 83 instead of Rs 78,
more gain = 83 - 78 = Rs. 5
given that more gain = 20%.

 \frac{5}{x} \times 100 = 20\\ \\ \Rightarrow \frac{500}{x}=20  \\ \\ \Rightarrow x =  \frac{500}{20}=Rs.\ 25

So Cost price is Rs. 25

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