Question

A man sells a mare for Rs. 1085 making a profit \[8\dfrac{1}{2}\]%. The cost of the mare is:
(a) Rs. 982
(b) Rs. 999.50
(c) Rs. 927.75
(d) Rs. 1000

Answer 1

Hint: To solve the given question, we will first find out what profit is. Then we will convert the given profit percentage from mixed fraction into an improper fraction. Then we will find the profit by using the formula Profit = SP – CP, where SP is the selling price of the mare and CP is the cost price on the mare. Then, we will find the profit % by the formula: \[\text{Profit Percent}=\dfrac{\text{Profit}}{\text{CP}}\times 100.\] In this formula, we will substitute the value of profit and we will obtain the value of the cost price of the mare.

Complete step by step answer:
To start with, we will first find out what profit is and what the formula to obtain profit is. Profit is defined as the amount gained on selling any item or goods. In other words, profit is the difference between the cost price and selling price of the item. The formula to calculate the profit on any item is as shown below.
Profit = Selling Price – Cost Price
Now, let us assume that the cost price of the mare is x. Thus, we will get the following equation
\[\text{Profit}=1085-x.....\left(i \right)\]
Now, it is given that the profit percentage is \[8\dfrac{1}{2}\]%. We will convert it from mixed fraction to improper fraction. If the mixed fraction is of the form \[x\dfrac{y}{z},\] then its improper fraction will be \[\dfrac{zx+y}{z}.\] Thus, we will get,
\[8\dfrac{1}{2}\text{ Percent}=\dfrac{\left( 8\times 2 \right)+1}{2}\text{ Percent}\]
\[\Rightarrow 8\dfrac{1}{2}\text{ Percent}=\dfrac{17}{2}\text{ Percent}\]
Now, we have to calculate the profit percentage. The profit percentage is given by the formula
\[\text{Profit Percent}=\dfrac{\text{Profit}}{\text{Cost Price}}\times 100\]
In our case, \[\text{Profit Percent}=\dfrac{17}{2}\text{ Percent,}\] cost price = x and profit = 1085 – x. On substituting these values in the above formula, we get,
\[\Rightarrow \dfrac{17}{2}=\dfrac{1085-x}{x}\times 100\]
\[\Rightarrow \dfrac{17}{2}=\left( \dfrac{1085-x}{x} \right)100\]
\[\Rightarrow \dfrac{17}{200}=\dfrac{1085-x}{x}\]
\[\Rightarrow 17x=200\left( 1085-x \right)\left[ \text{On cross multiplication} \right]\]
\[\Rightarrow 17x=217000-200x\]
\[\Rightarrow 200x+17x=217000\]
\[\Rightarrow 217x=217000\]
\[\Rightarrow x=\dfrac{217000}{217}\]
\[\Rightarrow x=Rs.1000\]
Thus, the cost of the mare is Rs. 1000.

So, the correct answer is “Option D”.

Note: Students should not get confused with cost price and selling price. Some students forget to take cost price in denominator.