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Word Problem 5_

Problem 5: A dealer sales a shirt and gets a profit of 15%. Had he sold it for Rs 4 more, he would have earned profit of 5% more. What is the cost price of the shirt?



Solution:

Let CP of Shirt =x

Profit =P= 15% of x

So it means by formula;

SP = P+CP

SP = 15% of x + x

\Rightarrow SP= \frac{15}{100}x+x

\Rightarrow SP= \frac{15x+100x}{100}

\Rightarrow SP= \frac{115x}{100}

Now according to condition – if he had sold it for 4 Rs more, i-e with   SP= \frac{115x}{100}+4 , he would earn profit of 20% ( 4% more than earlier!)

So, in this case;

CP=x

 SP= \frac{115x}{100x}+4

P= 20 % of x

Again using formula for profit

P= SP-CP

P=( \frac{115x}{100}+4)-x

\Rightarrow P=( \frac{115x+400-100x}{100})

\Rightarrow P=( \frac{15x+400}{100})

Taking 100 to LHS

\Rightarrow 100 \times P=15x+400

Now ,

P= \frac{20}{100}x

put in above;

\Rightarrow 100 \times \frac{20}{100}x =15x+400

\Rightarrow 20x =15x+400

\Rightarrow 20x -15x=400

\Rightarrow 5x=400

\Rightarrow x=\frac{400}{5}

\Rightarrow x=80 Rs

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