Question

Pavithra bought some books for rupees 60. Had she bought 5 more books for the same amount each book would have cost her 1 rupee less find the number of books bought by pavithra and price of each book

Answer 1

Let the number of books be x
Number of books brought for ₹60 = x
Cost of one book = 60/x
Now,the cost of each book is reduced by ₹1
Number of books brought for ₹60 = x+5
A/Q
60/x - 60/x+5 = 1
60(1/x - 1/x+5) = 1
60[x+5 - x/x(x+5) ] = 1
60[5/x(x+5) ] = 1

${x}^{2} + 5x = 300$
${x}^{2} + 5x - 300 = 0$
${x}^{2} + 20x - 15x - 300 = 0$
x(x+20) - 15(x+20) = 0
(x-15)(x+20) =0
x-15=0
x= 15
Number of books = 15

Answer 2

Answer:

The cost of each book is Rs 4 and total number of books purchased were 15.

Step-by-step explanation:

Let the cost of each book = x

Let number of books = y

Hence xy = 60

=> y = 60/x

After the price reduction new price = x-1

Total number of books = y + 5

Hence we get,

(x-1)(y+5) = 60

=> xy +5x - y -5 = 60

=> 60 + 5x - 60/x -5 = 60

=> 5x - 60/x -5 = 0

=> x -12/x - 1 = 0

=> x² - x -12 = 0

=> x =  4 or -3

rejecting -3 we get x = 4

=> y = 60/4 = 15

Hence the cost of each book is Rs 4 and total number of books purchased were 15