Question

On sale with a 20% discount, the price of a book is $40. What is the original price of the book?

• A. $\$50$
• B. $\$40$
• C. $\$32$
• D. $\$25$

Answer 1

The correct option is A $\$50$

Let the original price of the book is $S,$ then

Discount amount of the book
$=20\%\text{of}S=\frac{20}{100}\times S=\frac{20}{20\times 5}\times S$
$=\frac{1}{5}\times S$
$=\frac{S}{5}$

Given, price of the book after discount $=\$40$
$\therefore \text{Original price of the book - Discount amount = Price of the book after discount}$
$\Rightarrow S-20\%\text{of}S=40$

$\Rightarrow S-\frac{S}{5}=40$

$\Rightarrow \frac{S\times 5}{5}-\frac{S}{5}=40(\because \text{Taking LCM to subtract})$

$\Rightarrow \frac{5S-S}{5}=40$

$\Rightarrow \frac{4S}{5}=40$
Cross multiplying, we get
$4S=40\times 5$

Dividing both the sides by $4,$ we get
$\frac{4S}{4}=\frac{40\times 5}{4}$
$\Rightarrow S=\frac{4\times 10\times 5}{4}$
$\Rightarrow S=10\times 5\Rightarrow S=50$

Hence, original price of the book was $\$50.$