Question

An almirah is sold for 5400 Rs after allowing a discount of 10%. Find the marked price.

Answer 1

Hint: We will find the amount that was discounted using the discount percentage given. We will subtract this amount from the marked price to obtain the selling price of the almirah. Then we will form a linear equation using the selling price, marked price, and the discounted amount. We will solve this equation to obtain the marked price.

Complete step by step answer:
Let us assume that the marked price of the almirah is $x$ Rs. We know that a discount of 10% was given. So, we will now calculate 10% of the marked price as follows,
 $10\mathrm{\%}\text{ discount}={\displaystyle \frac{10}{100}}\times x\text{ Rs}$
This is the amount of discount that was allowed. Therefore, the selling price is the amount after subtracting the amount of discount from the marked price. So, we can form a linear equation using the selling price, marked price and the discounted amount in the following manner,
 $\text{selling price}=\text{marked price}-\text{discount amount}$
We will substitute the marked price as $x$ and the discount amount as ${\displaystyle \frac{10}{100}}\times x$ in the above equation. Then we get,
 $\text{selling price}=x-{\displaystyle \frac{10}{100}}\times x$
We are given that the selling price of the almirah is 5400 Rs. Substituting this value in the above equation, we get
 $5400=x-{\displaystyle \frac{10}{100}}\times x$
Simplifying the above equation and solving it for $x$ , we get
 $\begin{array}{rl}& 5400=x-{\displaystyle \frac{1}{10}}\times x\\ & \Rightarrow 5400={\displaystyle \frac{9}{10}}\times x\\ & \Rightarrow x={\displaystyle \frac{5400\times 10}{9}}\\ & \therefore x=6000\text{ Rs}\end{array}$
The marked price of the almirah is 6000 Rs.

Note:
 We should be familiar with the concept of discount and discount percentage. The discount is the important part which relates the marked price and the selling price. There is a similar concept of profit and profit percentage. The difference between profit and discount is that the discount is subtracted from the marked price and the profit is added to the marked price.