Question

The ratio between the sale price and the cost price of an article is 7 : 5. What is the ratio between the profit and the cost price of that article?
A. 2 : 7
B. 5 : 2
C. 7 : 2
D. 2 : 5

Answer 1

We will first assume the sale price and the cost price using the given ratio. Now, we can find profit using them and then we will just find the ratio of profit and cost price.

Complete step-by-step answer:
Since, we are given that the ratio of the sale price and cost price is 7 : 5.
Let the sale price of the article be 7x, so the cost price of the article will be 5x.
Now, we know we have the formula of profit given by the following expression:-
$\Rightarrow$Profit = Sale Price – Cost Price
If we put up the values, we assumed of the cost price and the sale price, we will then obtain:-
$\Rightarrow$Profit = 7x – 5x
We can write the above expression as:-
$\Rightarrow$Profit = (7 – 5)x
Simplifying the calculations in the above expression, we will then obtain:-
$\Rightarrow$Profit = 2x
Now, we are required to find the ratio of the profit and the cost price of the article that is we are required to find $\dfrac{{\Pr ofit}}{{C.P.}}$
Putting the value of cost price which we assumed and the profit as we found, we will then obtain the following expression:-
$\Rightarrow \dfrac{{\Pr ofit}}{{C.P.}} = \dfrac{{2x}}{{5x}}$
Now we can cancel out x from both the numerator and denominator, we will get:
$\Rightarrow$Profit : Cost Price = 2 : 5.
Hence, the required ratio is 2 : 5.

Hence, the correct option is (D).

Note:
The students must note that we basically cancelled out x from both the numerator and denominator in the last third step, we could do that because we know that x is not equal to 0. Because if x would have been 0, that means the cost price, sale price and profit, all of that is 0, so we basically get a contraction to the ratio given to us as well.