Question

# A rise of 25% in the price of sugar, compels a man to buy 5 kg sugar less for Rs. 200. Calculate the increased price per Kg.

Hint: In this particular question use the concept that assume any variable be the price of sugar per kg and assume any different variable be the amount of sugar he purchased, then use the concept that the total amount he spent is the equal to the product of price of sugar per kg and amount of sugar he purchased so use these concepts to reach the solution of the question.

Complete step by step answer:
Let the price of the sugar be X Rs. per Kg.
And let the man buy Y kg of sugar.
So the amount of sugar he buys for Rs. 200 is
200 = XY............... (1)
Now it is given that there is a rise of 25% in the price of sugar.
So the price of the sugar becomes = (X + $\dfrac{{25}}{{100}}$ X) Rs/Kg.
Now due to this he has to buy 5 Kg less sugar.
So the amount of sugar he bought = (Y – 5) Kg.
The total amount he has to spend is the same i.e. 200 Rs.
Therefore, 200 = $\left( {X + \dfrac{{25}}{{100}}X} \right)\left( {Y - 5} \right)$
Now simplify we have,
$\Rightarrow 200 = \dfrac{5}{4}XY - \dfrac{{25}}{4}X$
Now substitute the value of XY from equation (1) in the above equation we have,
$\Rightarrow 200 = \dfrac{5}{4}\left( {200} \right) - \dfrac{{25}}{4}X$
Now simplify we have,
$\Rightarrow \dfrac{{25}}{4}X = \dfrac{5}{4}\left( {200} \right) - 200$
$\Rightarrow \dfrac{{25}}{4}X = \dfrac{1}{4}\left( {200} \right)$
$\Rightarrow X = \dfrac{{200}}{{25}} = 8$ Rs/kg.
So the original price of the sugar is 8 Rs/Kg.
Now we have to calculate the increased price per Kg.
So the increased price is the sum of the original price of the sugar and the 25% of the original price of the sugar per kg.
Therefore, increased price per kg = $8 + 8\left( {\dfrac{{25}}{{100}}} \right) = 8 + \dfrac{8}{4} = 8 + 2 = 10$ Rs/Kg.

So the increased price per Kg is Rs. 10.

Note: Whenever we face such types of questions the key concept we have to remember is that increased price is the sum of the original price of the sugar and the 25% of the original price of the sugar per kg, so first calculate the original price of sugar as above, then substitute this value in the above described formula and simplify we will get the required answer.