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# A reduction of 25% in the price of an article enables a man to buy 50 kilograms more for Rs. 500. What is the reduced price per kilogram?(a) Rs. 3(b) Rs. 2.5(c) Rs. 2.05(d) Rs. 2.4  Hint: It is a word problem related to the money exchange, and the only thing that we need to focus on for solving this problem is the percentage calculation.

To start with the solution, we let the original price of the article per kilogram to be Rs. x. Let the quantity in kilogram, bought initially without reduction be y.
Now we know the product of cost per kilogram and quantity is equal to the money paid.
$\therefore xy=500$
$\Rightarrow y=\dfrac{500}{x}............(i)$
The reduction that was given = 25% of its original price = $\dfrac{25}{100}\times x$
Reduced price of the article = original price – reduction= $x-\dfrac{25}{100}\times x=\dfrac{75}{100}x=\dfrac{3}{4}x$

Now the question states that a reduction of 25% in the price of an article enables a man to buy 50 kilograms more for Rs. 500. Representing it mathematically, we get
$\dfrac{3}{4}x\times \left( y+50 \right)=500$
Now we will substitute the value of y from equation (i). On doing so, we get
$\dfrac{3}{4}x\times \left( \dfrac{500}{x}+50 \right)=500$
$\Rightarrow \dfrac{3}{4}\times \left( \dfrac{500+50x}{{}} \right)=500$
$\Rightarrow 3\times \left( 10+x \right)=40$
$\Rightarrow 3x+30=40$
$\Rightarrow 3x=10$
$\Rightarrow x=\dfrac{10}{3}$
Therefore, reduced price = $\dfrac{3}{4}\times x=\dfrac{3}{4}\times \dfrac{10}{3}=\dfrac{10}{4}=Rs.\text{ 2}\text{.5}$
Hence, the answer to the above question is option (b) Rs. 2.5.

Note: Don’t get confused and take the percentages with respect to selling price while solving, as we should be very clear that the percentage loss or profit are terms related to the actual pricing not to the price for which we crack the deal. The other way of thinking of this is selling price might vary from buyer to buyer depending on the bargain they put in, but the percentage should be defined from a fixed mark so that we can easily handle it. For example: most products in the market have an MRP tag on it, making it easier for all the sellers to handle their margins.
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