Question

A book was on sale for 30% off its original price. If the sale price of the book was $28, what was the original price of the book? (Assuming there is no sales tax)*

Answer 1

Given :

Selling price of a book : $28

Discount percentage of the book : 30%

To find :

The original price of the book.

Solution :

We can find the value of original price of the book by different ways. The first way is to find the value of it by taking variables.

Discount amount of book :

Let the original price be x.

$\sf \dashrightarrow 30\% \: of x$

$\sf \dashrightarrow \dfrac{30}{100} \times x$

$\sf \dashrightarrow \dfrac{3}{10} \times x$

$\sf \dashrightarrow \dfrac{3x}{10}$

Now, we can find the value of it's original price.

Original price of the book :

$\sf \dashrightarrow SP = CP - Discount$

$\sf \dashrightarrow 28 = x - \dfrac{3x}{10}$

$\sf \dashrightarrow 28 = \dfrac{10x - 3x}{10}$

$\sf \dashrightarrow 28 = \dfrac{7x}{10}$

$\sf \dashrightarrow 7x = 28 \times 10$

$\sf \dashrightarrow 7x = 280$

$\sf \dashrightarrow x = \dfrac{280}{7}$

$\sf \dashrightarrow x = 40$

Now, we'll find out the same by an other way which is by using the formulae.

$\sf \dashrightarrow CP = \dfrac{100}{(100 - Loss\%)} \times SP$

$\sf \dashrightarrow \dfrac{100}{(100 - 30)} \times 28$

$\sf \dashrightarrow \dfrac{100}{70} \times 28$

$\sf \dashrightarrow \dfrac{10}{7} \times 28$

$\sf \dashrightarrow \dfrac{10 \times 28}{7} = \dfrac{280}{7}$

$\sf \dashrightarrow \cancel \dfrac{280}{7} = 40$

Hence, the original price of the book is $40.

Answer 2

Given:

The discount percentage of the book was 30% and the sale price of the book was $28.

To find:

Original price of the book.

Solution:

To solve this question,

Let the original price of the book be 100units.

As the selling price of the book is 30% off of the original price (100%)

This means, discount on the book is=

$\frac{30}{100} \times 100 = 30units$

Hence, the selling price of the book is= (100-30)units= 70units. (i)

But according to the question, the selling price of the book is $28. (ii)

So, after equating (i) and (ii) values, we get

$70units = 28$

$1unit = \frac{28}{70}$

As the original price of the book is 100units, so

$100units = \frac{28}{70} \times 100$

= $40.

Hence, the original price of the book was $40.