Question

Anirudh bought some books for Rs.60.had he bought 5 more books for the some amount each book would have cost him 1 rupee less. Find the number of the books bought by anirudh and the price of each book.

Answer 1

5 book and 12 rupees is the price of each book

Answer 2

Let the number of books be x

Cost of all books = 60

∴ cost of one book = 60/x ------ ( i )

Now, Number of books x + 5 (if he purchases 5 more books)

Cost of one book = 60/(x+5) ------ ( ii )

According to question New cost is 1 less than the earlier cost of the book

∴ Earlier Cost of the book - New cost of the Book = 1

$\frac{60}{x} - \frac{60}{x+5} = 1$

$\frac{60(x+5)-60x}{x(x+5)}=1$

$\frac{60x+300-60x}{x^2+5x}=1$

$x^2 +5x-300=0$

$x^2 +20x-15x-300=0$

$x(x+20)-15(x+20)=0$

$(x+20)(x-15)=0$

x + 20 = 0   ;     x - 15 = 0

x = -20, 15

∵ Number of Books can not be negative therefore neglecting x = -20

Number of books purchased = 15

Cost of one book = 60 / 15 = Rs.4