Question

A dishonest dealer sells his goods at the cost price but uses 20 % less weight. What is his profit or loss %?
(a) 22.5 %
(b) 12.5 %
(c) 25 %
(d) 50 %

Answer 1

Hint: To solve the given question, we will first assume that the actual weight of the goods which the dealer sells is y kg and the weight of the goods which he should sell is x kg with the help of the information given in the question. Then we will assume that the price of 1 kg of goods is z. With the help of this, we will find the price of y and x kg of goods. After getting the price, we will find the profit by subtracting y from x. Then, we will divide the profit by y and multiply by 100 to get the profit percent.

Complete step-by-step answer:
To start with we will assume that the actual weight of the goods the dealer is selling is y kg and the amount of goods which he should be honestly selling is x kg. Now, we are given the question that y is 20 % less than x, i.e. y is 80 % of x. Thus, we will get,
y = 80 % of x
\[\Rightarrow y=\dfrac{80}{100}\times x\]
\[\Rightarrow y=\dfrac{4x}{5}.....\left( i \right)\]
Now, we are going to assume that the price of 1 kg of goods is z. Thus, the price of y kg of goods will be yz and the price of x kg of goods will be xz.
Now, we can say that the dealer buys some goods at the price of yz and sells it at the price of xz. As the value of x will be greater than y, the dealer will get profit on selling y kg of goods. We know that profit is the difference between the selling price and the cost price of goods. Thus, we will get,
Profit = Selling Price – Cost Price
\[\Rightarrow \text{Profit}=xz-yz\]
\[\Rightarrow \text{Profit}=z\left( x-y \right).....\left( ii \right)\]
Now, we have to calculate the profit percent. The profit percent is obtained by dividing the profit with the cost price and multiplying by 100. Thus, we will get,
\[\Rightarrow \text{Profit Percent}=\dfrac{\text{Profit}}{\text{Cost Price}}\times 100\text{ Percent}\]
From (ii), we will get,
\[\Rightarrow \text{Profit Percent}=\dfrac{z\left( x-y \right)}{yz}\times 100\text{ Percent}\]
\[\Rightarrow \text{Profit Percent}=\dfrac{x-y}{y}\times 100\text{ Percent}\]
Now, we will put the value of y from (i) to the above equation. Thus, we will get,
\[\Rightarrow \text{Profit Percent}=\dfrac{x-\dfrac{4x}{5}}{\dfrac{4x}{5}}\times 100\text{ Percent}\]
\[\Rightarrow \text{Profit Percent}=\dfrac{\dfrac{x}{5}}{\dfrac{4x}{5}}\times 100\text{ Percent}\]
\[\Rightarrow \text{Profit Percent}=\dfrac{1}{4}\times 100\text{ Percent}\]
\[\Rightarrow \text{Profit Percent}=25\text{ Percent}\]

Note: We can also solve the question in an alternate way as shown. Let the actual weight of the goods he is selling is ‘a’. This is 80 % of the good which he should be honestly selling which is ‘b’. Thus,
a = 80 % of b
\[\Rightarrow a=\dfrac{4}{5}\text{ of b}\]
\[\Rightarrow a=\dfrac{4b}{5}\]
\[\Rightarrow \dfrac{5a}{4}=b\]
\[\Rightarrow a+\dfrac{a}{4}=b\]
\[\Rightarrow a=b-\dfrac{a}{4}\]
Now, we can see that the dealer is selling \[\dfrac{a}{4}\] less good in the same price. Thus, the profit percentage will be
\[\Rightarrow \text{Profit Percent}=\dfrac{\left( \dfrac{a}{4} \right)}{a}\times 100\text{ Percent}\]
\[\Rightarrow \text{Profit Percent}=\dfrac{1}{4}\times 100\text{ Percent}\]
\[\Rightarrow \text{Profit Percent}=25\text{ Percent}\]