Question

purchase book some books for rupees 120 if she purchased 3 more book for same amount each book would have cost rupees to less find the number of book purchase by Sunny and each price of the book​

Answer 1

Answer:

he will buy 3 more books each of rupees 40

Answer 2

The correct question is : Sunny purchased some books for rupees 120. If she purchased 3 more books at the same amount, then each book would have cost rupees 2 less. Find the number of books purchased by Sunny and cost price of each book​.

Given :

Total cost price of books purchased by Sunny = Rs. 120

To find :

(i) The number of books bought by Sunny.

(ii) Cost price of each book.

Solution :

• Let the number of books purchased by Sunny be x.

• Cost price of x books = Rs. 120

=> Cost price of each book = Rs. 120 / x

• If Sunny had purchased three more books at Rs. 120, then the number of books would be x + 3.

• New cost price of each book = Rs. 120 / (x + 3)

• According to the question, the following equation can be formed :

$\frac{Rs. 120}{x + 3} = \frac{Rs. 120}{x} - Rs.2\\\\=> \frac{Rs.120}{x} - \frac{Rs.120}{x + 3} = Rs.2\\\\=> Rs.120 \ [\frac{1}{x} - \frac{1}{x + 3} ] = Rs.2\\\\=> 120 \ [ \frac{x+ 3- x}{x(x + 3)} ] = 2\\\\=> 120 \ [ \frac{3}{x^{2}+ 3x } ] = 2\\\\=> 120 \ . \ 3 = 2 (x^{2} + 3x)\\\\=> \frac{120 \ . \ 3}{2} = x^{2} + 3x\\\\=> 60 \ . \ 3 = x^{2} + 3x\\\\=> 180 = x^{2} + 3x\\\\=> x^{2} + 3x - 180 = 0\\\\=> x^{2} + 15x - 12x - 180 = 0\\\\=> x (x + 15) + 12 (x + 15) = 0\\\\=> (x + 15) \ (x + 12) = 0$

$\\=> x + 15 = 0 \ ; \ x - 12 = 0\\\\=> x = - 15 \ ; \ x = 12$

• Since the number of books cannot be negative, - 15 is discarded.

∴ Number of books purchased by Sunny = 12

• Cost price of each book = Total cost price of books / Number of books

= Rs. 120 / 12

= Rs. 10

∴  Cost price of each book purchased by Sunny = Rs. 10