Question

pls answer this question​

Answer 1

★${\red{\underline{\huge{\mathbb{Question:-}}}}}$★

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 Shanvi and price of each book.

★${\red{\underline{\huge{\mathbb{Solution:-}}}}}$★

Consider,

The numbers of books→ x

So,

$\tt{X\: books\: have\: been\: purchased\: for\: Rs.\:=120}$

$\tt{1\: book\: has\: been\: purchased\: for\: Rs.\:=\:120/x}$

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•Sanvi purchased 3 more books for the same amount.

Now, the number of books=(x+3)

$\tt{(x+3)\: books\: have\: been\: purchased\: for\: Rs.\:=120}$

$\tt{1\: book\: has\: been\: purchased\: for\: Rs.\:=\:120/(x+3)}$

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According to the question,

$\frac{120}{x} - \frac{120}{x + 3} = 2 \\ = > \frac{120x + 360 - 120x}{x(x + 3)} = 2 \\ = > \frac{360}{ {x}^{2} + 3x} = 2 \\ = > 2 {x}^{2} + 6x = 360 \\ = > 2 {x}^{2} + 6x - 360 = 0 \\ = > {x}^{2} + 3x - 180 = 0 \\ = > {x}^{2} + 15x - 12x - 180 = 0 \\ = > (x + 15)(x - 12) = 0$

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x-12=0

=> x = 12

★ $\tt\boxed{Numbers\: of \:the\: books\: purchased\: by\: Sanvi\:= 12}$

So, Price of 12 books = ₹120

Price of 1 book = ₹120/12

= ₹10

★$\tt\boxed{Price\: of\: each\: book\:= 10\: rupees}$

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★${\red{\underline{\huge{\mathbb{Answer:-}}}}}$★

• Numbers of books= 12.

• Price of each book = ₹ 10

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