Question

In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?

Answer 1

Hint: In this particular question assume any variable be the cost price of the wine and use the concept that profit in Rs. is the multiplication of cost price in Rs. and the percentage of profit, so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Now,
Let us assume initially there is one liter of wine.
And let the cost price of the wine be x Rs/lit.
Now it is given that we have to make a profit of 33.33% when we sell the mixture of water and wine at the cost price of wine.
So we have to calculate the ratio of water to wine so that we can make 33.33% profit.
Now as we know that the profit in Rs/lit is the multiplication of cost price in Rs/lit and the percentage of profit.
So profit in Rs/lit = $x\left( {\dfrac{{33.33}}{{100}}} \right) = \dfrac{x}{3}$ Rs/lit.
Now let us use W amount of water in the mixture.
So the ratio of water to wine = (W : 1).
So the total amount of liquid in the new mixture is (W + 1) lit.
Now we have to sell it at the original cost price of the wine.
So the cost of mixture is $\left( {W + 1} \right)x$ Rs....................... (1)
And the selling price of the mixture is = original cost of wine + profit which we want.
So the selling price of the mixture = $x + \dfrac{x}{3} = \dfrac{{4x}}{3}$Rs/lit................ (2)
Now the selling price is equal to the cost price according to the question.
So, equate equation (1) and (2) we have,
$ \Rightarrow \left( {W + 1} \right)x = \dfrac{{4x}}{3}$
$ \Rightarrow \left( {W + 1} \right) = \dfrac{4}{3}$
$ \Rightarrow W = \dfrac{4}{3} - 1 = \dfrac{1}{3}$Lit.
So the ratio of water to wine is
$ \Rightarrow {\text{water : wine = }}\dfrac{{\dfrac{1}{3}}}{1} = 1:3$
So we have to mix water and wine in the ratio (1 : 3) so that if we sell the mixture at the cost price of wine we get 33.33% of profit.
So this is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember in this question is that the selling price of the mixture is the sum of the original cost of wine and the profit which we want, and according to question the selling price of the mixture is equal to the cost price of the mixture, so equate them as above we will get the required amount of water then we easily get the ratio of water and wine such that we made a profit of 33.33% after selling the mixture at the cost price of the wine.