Question

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A shopkeeper buy certain number of books in ₹80 if he buy 4 more books then new cost price of each book is reduced by ₹1 .find the numbers of book intially he buy?




➝ REQUIRED GOOD ANSWER ✔​

Answer 1

Answer:

the shopkeeper brought 16 books

Step-by-step explanation:

Let the shopkeeper buy x number of books.

According to the given condition cost of x books =Rs80

Therefore cost of each book =x80

Again when he had brought 4 more books

Then total books in this case =x+4

So cost of each book in this case =x+480

According to Question,

x80−x+480=1

x(x+4)80(x+4)−80x=1

x2+20x−16x−320=0

(x−16)(x+20)=0

x=16orx=−20

Answer 2

QuestioN :

A shopkeeper buy certain number of books in ₹80 if he buy 4 more books then new cost price of each book is reduced by ₹1. Find the numbers of book intially he buy?

GiveN :

• A shopkeeper buy certain number of books in ₹80
• He buy 4 more books then new cost price of each book is reduced by ₹1.

To FiNd :

• The total numbers of book intially he buy?

ANswer :

The total number of books is 16.

SolutioN :

Let the number of books bought be x.

Then, the cost of x books = Rs. 80

⇒$Cost \:of \:1 \: book =Rs. \frac{80}{x}$

If he would have bought 4 more books, then

$Cost\: of\:one\:book=Rs.\frac{80}{x+4}$

It is given that the cost of one book is reduced by 1 rupee,

⇒$\frac{80}{x} -\frac{80}{x+4} =1$

⇒$80(\frac{1}{x}-\frac{1}{x+4}=1 )$

⇒$\frac{320}{x^{2} +4x} =1$

⇒ x² + 4x - 320 = 0

⇒ x = -20 OR x = 16

Rejecting x = -20, as number of books cannot be negative.

x = 16

∴Hence, the number of books is 16.