Q9. If the price of a book is reduced by Rs. 5, a person can buy 5 more books for Rs. 300. Find the original list price of the book.
Answers
Step-by-step explanation:
Given :-
If the price of a book is reduced by Rs. 5, a person can buy 5 more books for Rs. 300.
To find :-
Find the original list price of the book ?
Solution :-
Let the original list price of a book be Rs. X
Number of books are for Rs. 300
=> Amount / Cost of 1 book
=> Number of books = 300/X
The amount to be reduced in the list price = Rs. 5
Then the cost price of the book = Rs. (X-5)
Number of books are for Rs. 300
=> 300/(X-5)
According to the given problem
If the price of a book is reduced by Rs. 5, a person can buy 5 more books for Rs. 300.
=> [300/(X-5)] +5 = (300/X)
=> [300/(X-5)] -(300/X) = 5
=> [300X -300(X-5)]/(X(X-5)) = 5
=> (300X-300X+1500)/(X²-5X) = 5
=> 1500/(X²-5X) = 5
=> 1500 = 5(X²-5X)
=> 1500/5 = X²-5X
=>300 = X²-5X
=> X²-5X-300 = 0
=> X²-20X+15X-300 = 0
=> X(X-20)+15(X-20) = 0
=> (X-20)(X+15) = 0
=> X-20 = 0 or X+15 =0
=> X = 20 or X = -15
X can not be negative.
=> X = 20
Therefore, The list price = Rs. 20
Answer:-
The original list price of the book for the given problem is Rs. 20
Check:-
List price = Rs. 20
Number of books for Rs. 300 = 300/20 = 15
If Rs. 5 is reduced in the list price then the new price is 20-5 = Rs. 15
Number of books for Rs. 300 = 300/15 = 20
5 more books would be purchased
Verified the given relations in the given problem.