Question

Sanvi purchase some books for RS 120
If she purchased 3 more books for the same amount each book would have cost her RS 2 less find the number of books purchased by sanvi and the price of each book

Answer 1

Answer:

cost of book is 10rs

Explanation:

Step 1:

It is given that Sanvi purchased some books for Rs. 120

Let the no. of books purchased by Sanvi be "x".

So,

The cost of each book = Rs. [120/x] ...... (i)

Step 2:

Also given that she purchases 3 more books for the same price

Now, the no. of books with Sanvi will be "(x+3)".

and,

The cost of each book will be = Rs. [120/(x+3)] ...... (ii)

Step 3:

According to the question and substituting the values from (i) & (ii), we get

[120/x] - [120/(x+3)] = 2

⇒ 120 [(x+3-x)/x(x+3)] = 2

⇒ 60 [3/(x² + 3x)] = 1

⇒ 180 = x² + 3x

⇒ x² + 3x - 180 = 0

⇒ x² + 15x - 12x - 180 = 0

⇒ x(x+15) - 12(x+15) = 0

⇒ (x + 15)(x - 12) = 0

⇒ x = - 15 or 12

neglecting the negative value

⇒ x = 12 ← no. of books purchased by Sanvi

∴ The cost of each book = 120/x = 120/12 = Rs. 10