Question

Sanvi purchased some books for Rs. 120. If she purchased 3 more books
for the same amount each book would have cost her Rs. 2 less. Find the
number of books purchased by Sanvi and the price of each book.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• Sanvi purchased some books for Rs. 120

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• If she purchased 3 more books for the same amount each book would have cost her Rs. 2 less

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$\red{\underline \bold{To \: Find:}}$

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• Number of book sanvi purchased and the price of each book.

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let Sanvi purchased 'x' numbers of books.

Let the price of 1 book be 'y'

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$\underline{\bold{\texttt{We know that :}}}$

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$\red{\bold{Cost \: of \: 1 \: book \: = \: \dfrac {total \: cost } { total \: books \: purchased } }}$

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$\underline{\bold{\texttt{Cost of 1 book :}}}$

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$\bf \dashrightarrow y = \dfrac { 120 } { x }$ -----(1)

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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If she purchased 3 more books for the same amount each book would have cost her Rs. 2 less.

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Hence,

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$\sf \longmapsto \dfrac { 120 } { x + 3 } = y - 2$

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$\bf \dashrightarrow \dfrac { 120 } { x + 3 } + 2 = y$ ------(2)

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$\underline{\bold{\texttt{We got that :}}}$

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$\purple{\bold{Equation \: (1) \: = \: Equation \: (2)}}$

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$\sf \longmapsto \dfrac { 120 } { x + 3 } + 2 = \dfrac { 120 } { x }$

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$\sf \longmapsto \dfrac { 120 + 2x + 6 } { x + 3 } = \dfrac { 120 } { x }$

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$\sf \longmapsto 120x + 2x^2 + 6x = 120x + 360$

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$\sf \longmapsto 2x^2 + 6x - 360 = 0$

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$\underline{\bold{\texttt{Dividing the above equation by 2}}}$

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$\sf \dashrightarrow x^2 + 3x - 180 = 0$

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$\underline{\bold{\texttt{Splitting middle term}}}$

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$\sf \longmapsto x^2 + 15x - 12x - 180 = 0$

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$\sf \longmapsto x(x + 15) -12(x + 15)$

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$\sf \longmapsto (x - 12)(x + 15)$

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• x = 12

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• x = -15

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As number of books can't be negative, Hence x = 12

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$\underline{\bold{\texttt{Putting x = 12 in (1)}}}$

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$\sf \longmapsto y = \dfrac { 120 } { 12 }$

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$\bf \dashrightarrow y = 10$

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Hence she purchased 12 books and price of each book is 10 rupees

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$\rule{200}5$