Question

A burger shop sells two types of burger, A and B. The selling price of burger A is Rs 17, and burger B is Rs 13. Ingredient costs for burger A are Rs 450 per week, and for burger B are Rs 310 per week. Assuming the shop sells an equal number of both burgers in one week, at what point will profits for one burger overtake the other?
A) After 35 burgers each, burger B profits will overtake burger A profits
B) After 145 burgers each, burger B profits will overtake burger A profits
C) After 35 burgers each, burger A profits will overtake burger B profits
D) After 145 burgers each, burger A profits will overtake burger B profits

Answer 1

Hint: In types of questions, we have to consider a variable for the number to be find, and from the data given in the question we will get two linear equations in the variable and we have to solve these equations by taking all variable terms to one side and all constants to one side, to get the value of the required variable.

Complete answer:
Given a burger shop sells two types of burger, A and B, and the selling price of burger A is Rs17, and of burger B is Rs13. Ingredient costs for burger A are Rs450 per week, and for burger B are Rs310 per week, and the shop sells an equal number of both types of burgers in one week.
Let us consider that the shop sells $x$ number of burger A and $x$ number of burger B as the shop sells an equal number of burgers in one week.
Now given that the selling price of burger A is Rs17, and the selling price of burger B is Rs13, and the costs of ingredients for burger A are given by Rs450 and the costs of ingredients for burger B are given by Rs310.
From the given data of the above question we can write,
The profit for burger A$ = 17x - 450$,
The profit for burger B$ = 13x - 310$,
Now let us assume that the profits for both the burgers are equal, then the equations should be equal, i.e.,
$17x - 450 = 13x - 310$
Now taking $x$ terms to one side we get,
$ \Rightarrow 17x - 13x = 450 - 310$
Now subtracting we get,
$ \Rightarrow 4x = 140$
Now dividing both sides with 4 we get,
$ \Rightarrow \dfrac{{4x}}{4} = \dfrac{{140}}{4}$

Now simplifying we get,
$ \Rightarrow x = 35$.
So, from the calculation when the number of burgers sold are equal to or greater than 35, then the profits of burger A will overtake the profits of burger B.
So, option C is correct i.e., After 35 burgers each, burger A profits will overtake burger B profits

After selling 35 burgers of each type i.e., burger A and burger B, the profits of burger A will overtake the profits of burger B.

Note:
The profit and loss problems will be mainly depends on the formulas related profit percentage and loss
percentage and calculation of profit and loss, some of the useful formulas are given here:
Profit = Selling price\[ - \]cost price,
Loss =Cost price\[ - \]selling price,
Profit%\[ = \dfrac{{S.P - C.P}}{{C.P}} \times 100\% \],
Loss%\[ = \dfrac{{C.P - S.P}}{{C.P}} \times 100\% \].