Question

The difference between two selling prices of a jacket at profits \[4\% \] and \[5\% \] is Rs. 6. Find the cost price of the jacket and two selling price of the jacket.

Answer 1

Hint:
Here, we will first assume the cost of each jacket is Rs. \[x\]. Then we will add the cost of each jacket with the profits of first jacket cost to find the selling price of the first jacket and then add the cost of each jacket with the profits of second jacket cost to find the selling price of the second jacket. Then take their difference equal to Rs 6 to find the required value.

Complete step by step solution:
We are given that the difference between the two selling prices of a jacket at profits \[4\% \] and \[5\% \] is Rs. 6.

Let us assume that the cost of each jacket is Rs. \[x\].

Now we will add the cost of each jacket with the profits of the first jacket cost to find the selling price of the first jacket, we get
\[
   \Rightarrow {\text{Selling price of first jacket}} = x + \dfrac{4}{{100}} \times x \\
   \Rightarrow {\text{Selling price of first jacket}} = x + \dfrac{x}{{25}} \\
   \Rightarrow {\text{Selling price of first jacket}} = \dfrac{{26x}}{{25}} \\
 \]

Adding the cost of each jacket with the profits of the second jacket cost to find the selling price of the second jacket, we get
\[
   \Rightarrow {\text{Selling price of second jacket}} = x + \dfrac{5}{{100}} \times x \\
   \Rightarrow {\text{Selling price of second jacket}} = x + \dfrac{x}{{20}} \\
   \Rightarrow {\text{Selling price of second jacket}} = \dfrac{{21x}}{{20}} \\
 \]

Since we are given that the difference between the selling price of the first jacket and the second jacket is Rs. 6, so we have
\[
   \Rightarrow \dfrac{{21}}{{20}}x - \dfrac{{26}}{{25}}x = 6 \\
   \Rightarrow \dfrac{{105x - 104x}}{{100}} = 6 \\
   \Rightarrow \dfrac{x}{{100}} = 6 \\
 \]

Multiplying the above equation by 100 on both sides, we get
\[
   \Rightarrow 100 \times \dfrac{x}{{100}} = 6 \times 100 \\
   \Rightarrow x = 600 \\
 \]

Hence, the cost price of each jacket is Rs. 600.

Substituting the value of cost jacket in the selling price of the first jacket and second jacket, we get
\[
   \Rightarrow {\text{Selling price of first jacket}} = \dfrac{{26}}{{25}} \times 600 \\
   \Rightarrow {\text{Selling price of first jacket}} = {\text{Rs. }}624 \\
 \]

\[
   \Rightarrow {\text{Selling price of second jacket}} = \dfrac{{21}}{{20}} \times 600 \\
   \Rightarrow {\text{Selling price of second jacket}} = {\text{Rs. }}630 \\
 \]

Hence, the cost price of each jacket is Rs. 600 and the selling prices of the two jackets are Rs. 624 and Rs. 630 respectively.

Note:
You have to subtract the selling price of the first jacket from the second jacket or else the answer will be wrong. Do not forget to write the unit in the final answer. Here, we use the word “of” is for multiplication while finding the cost price. It is important to remember that the sales price is the price on which the product is sold.