a person buys a number of books for rupees 80. if he had bought 4 more books for the same amount, each book would have cost rupees One Less. how many books did he buy?
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Case 1:
Let no. of books = x
Total price = Rs. 80
Price of each book = 80/x --- (i)
Case 2:
No. of books = x + 4
Total price = Rs. 80
Price of each book = 80 / (x + 4)
= (80 / x) - 1 [ From equation (i) ]
∴ 80 / (x+4) = ( 80 / x ) - 1
⇒ 80 / (x + 4) = (80 - x ) / x
⇒ 80 x = (80 - x) * (x + 4) [Cross Multiply]
⇒ 80 x = 80 (x + 4) - x (x + 4)
⇒ 80 x = 80 x + 320 - x² - 4 x
⇒ x² + 4 x - 320 = 0
⇒ x² - 16 x + 20 x - 320 = 0
⇒ x ( x - 16 ) + 20 ( x - 16 ) = 0
⇒ ( x + 20 ) * ( x - 16 ) = 0
∴ x = 16 , -20
Therefore no .of book = 16 [ No. of books cannot be negative ]
Let no. of books = x
Total price = Rs. 80
Price of each book = 80/x --- (i)
Case 2:
No. of books = x + 4
Total price = Rs. 80
Price of each book = 80 / (x + 4)
= (80 / x) - 1 [ From equation (i) ]
∴ 80 / (x+4) = ( 80 / x ) - 1
⇒ 80 / (x + 4) = (80 - x ) / x
⇒ 80 x = (80 - x) * (x + 4) [Cross Multiply]
⇒ 80 x = 80 (x + 4) - x (x + 4)
⇒ 80 x = 80 x + 320 - x² - 4 x
⇒ x² + 4 x - 320 = 0
⇒ x² - 16 x + 20 x - 320 = 0
⇒ x ( x - 16 ) + 20 ( x - 16 ) = 0
⇒ ( x + 20 ) * ( x - 16 ) = 0
∴ x = 16 , -20
Therefore no .of book = 16 [ No. of books cannot be negative ]
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