Question

sanvi purchased some books for Rs 120.If she purchased 3 more books for the same amount each book would have cost her Rs 2less.Find the number of books purchased by sanvi and the price of each book
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Answer 1

There are 15 books and cost of each book is Rs. 8.

Step-by-step explanation:

Since we have given that

Let the number of books be 'x'

Cost = Rs. 120

Cost of each book = $\dfrac{120}{x}$

if 3 more books are purchased.

So, the number of books becomes

x+3

Cost of each book = $\dfrac{120}{x}$

Cost would be Rs. 2 less.

So, new cost becomes

$\dfrac{120}{x}-2$

According to question, it becomes,

$(x+3)(\dfrac{120}{x}-2)=120\\\\x\times \dfrac{120}{x}-2x+\dfrac{360}{x}-6=120\\\\120-2x-6+\dfrac{360}{x}=120\\\\114-2x+\dfrac{360}{x}=120\\\\-2x^2+360=(120-114)x\\\\-2x^2+360=6x\\\\x^2-180=3x\\\\x^2-3x-180=0\\\\x=-12,15$

So, the number of books = 15

and cost of each book = $\dfrac{120}{15}=8$

Hence, there are 15 books and cost of each book is Rs. 8.

# learn more:

Sanvi purchased 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.​

https://brainly.in/question/15496551

Answer 2

Answer: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

Step-by-step explanation: