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Question

By increasing the list price of a book by ₹12, a person can buy 24 books less for ₹1728. The original price of the book was_____.

A
₹24
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B
₹20
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C
₹16
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D
₹18
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Solution

The correct option is A ₹24
Let the original price of the book be x.
The increased price of the book will be (x+12).
The total amount to be spent is 1728.

Number of books which can be purchased in the first case is 1728x and the number of books which can be purchased in the second case is 1728x+12.

Given, 1728x1728x+12=24
1728×12=24×x(x+12)
2x2+24x1728=0
x2+12x864=0

For a quadratic equation ax2+bx+c,
x=b±b24ac2a

Here a=1,b=12 and c=864

So, x=12±(12)24×1×8642×2

x=12±36002=12±602

x=24 or x=36

x cannot be a negative value. So x=24

So, the original price of the book = ₹24

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