Question

A person bought some articles at the rate of 5 per rupee and the same number at the rate of 4 per rupee. He mixed both the types and sold at the rate of 9 for 2 rupees. In this business he suffered a loss of Rs. 3. The total number of articles bought by him was
(a) 1090
(b) 1080
(c) 540
(d) 545

Answer 1

Hint: Let us suppose that the person bought x articles of both the types. Amount spent on the first and second type of article = $\dfrac{x}{5}$ and $\dfrac{x}{4}$. Total CP = \[\dfrac{9x}{20}\]. Now, Total SP = $2x\times \dfrac{2}{9}=\dfrac{4x}{9}$. Subtract this from the CP and equate to 3. Solve for x to get the final answer.

Complete step-by-step answer:
In this question, we are given that a person bought some articles at the rate of 5 per rupee and the same number at the rate of 4 per rupee. He mixed both the types and sold at the rate of 9 for 2 rupees. In this business he suffered a loss of Rs. 3.
We need to find the number of articles bought by him.
Let us suppose that the person bought x articles of both the types.
Amount spent on first type of article = $\dfrac{x}{5}$
Amount spent on first type of article = $\dfrac{x}{4}$
So, total amount spent = Total CP = \[\dfrac{x}{5}+\dfrac{x}{4}=\dfrac{9x}{20}\]
Now, Total SP = $2x\times \dfrac{2}{9}=\dfrac{4x}{9}$
We are given that he suffered a loss of Rs. 3.
Hence, $\dfrac{9x}{20}-\dfrac{4x}{9}=3$
$81x-80x=3\times 180$
$x=540$
Hence, option (c) is correct.

Note: In this question, it is very important to understand the language of the question as some can get confused by it. Also, remember that in this question, he suffered loss. So, here we used CP – SP = 3. Many students will use the general formula SP – CP. In this case equate this to -3.