Question

Shoba had bought some pens for 48 had she bought 4 pens less for the same amount then each pen would have cost her rs 2 more find the no of pens bought by shoba

Answer 1

Question :-

Shoba had bought some pens for Rs 48. Had she bought 4 pens less for the same amount then each pen would have cost her Rs 2 more. Find the number of pens bought by Shoba.

$\large\underline{\sf{Solution-}}$

Let assume that number of pens bought by Shoba be x.

Now, given that Shoba bought x pens for Rs 48.

So,

$\rm\implies \:Price \: of \: 1 \: pen \: = \: \dfrac{48}{x} - - - (1)$

Further given that, she purchased x - 4 pens for Rs 48.

So,

$\rm\implies \:Price \: of \: 1 \: pen \: = \: \dfrac{48}{x - 4} - - - (2)$

According to statement, Had she bought 4 pens less for the same amount then each pen would have cost her Rs 2 more.

$\rm \:\dfrac{48}{x - 4} - \dfrac{48}{x} = 2$

$\rm \:\dfrac{48x - 48(x - 4)}{x(x - 4)} = 2$

$\rm \:\dfrac{48x - 48x + 198}{x(x - 4)} = 2$

$\rm \:\dfrac{198}{x(x - 4)} = 2$

$\rm \: x(x - 4) = 96$

$\rm \: {x}^{2} - 4x = 96$

$\rm \: {x}^{2} - 4x - 96 = 0$

$\rm \: {x}^{2} - 12x + 8x - 96 = 0$

$\rm \: x(x - 12) + 8(x - 12) = 0$

$\rm \: (x - 12)(x + 8) = 0$

$\rm\implies \:x = 12 \: \: or \: \: x = - 8 \: \{rejected \}$

So, Shoba bought 12 pens for Rs 48

$\rule{190pt}{2pt}$

Additional information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

• If Discriminant, D > 0, then roots of the equation are real and unequal.

• If Discriminant, D = 0, then roots of the equation are real and equal.

• If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

• Discriminant, D = b² - 4ac

Answer 2

Step-by-step explanation:

Question :-

Shoba had bought some pens for Rs 48. Had she bought 4 pens less for the same amount then each pen would have cost her Rs 2 more. Find the number of pens bought by Shoba.

\large\underline{\sf{Solution-}}

Solution−

Let assume that number of pens bought by Shoba be x.

Now, given that Shoba bought x pens for Rs 48.

So,

\begin{gathered}\rm\implies \:Price \: of \: 1 \: pen \: = \: \dfrac{48}{x} - - - (1) \\ \end{gathered}

⟹Priceof1pen=

x

48

−−−(1)

Further given that, she purchased x - 4 pens for Rs 48.

So,

\begin{gathered}\rm\implies \:Price \: of \: 1 \: pen \: = \: \dfrac{48}{x - 4} - - - (2) \\ \end{gathered}

⟹Priceof1pen=

x−4

48

−−−(2)

According to statement, Had she bought 4 pens less for the same amount then each pen would have cost her Rs 2 more.

\begin{gathered}\rm \:\dfrac{48}{x - 4} - \dfrac{48}{x} = 2 \\ \end{gathered}

x−4

48

−

x

48

=2

\begin{gathered}\rm \:\dfrac{48x - 48(x - 4)}{x(x - 4)} = 2 \\ \end{gathered}

x(x−4)

48x−48(x−4)

=2

\begin{gathered}\rm \:\dfrac{48x - 48x + 198}{x(x - 4)} = 2 \\ \end{gathered}

x(x−4)

48x−48x+198

=2

\begin{gathered}\rm \:\dfrac{198}{x(x - 4)} = 2 \\ \end{gathered}

x(x−4)

198

=2

\begin{gathered}\rm \: x(x - 4) = 96 \\ \end{gathered}

x(x−4)=96

\begin{gathered}\rm \: {x}^{2} - 4x = 96 \\ \end{gathered}

x

2

−4x=96

\begin{gathered}\rm \: {x}^{2} - 4x - 96 = 0 \\ \end{gathered}

x

2

−4x−96=0

\begin{gathered}\rm \: {x}^{2} - 12x + 8x - 96 = 0 \\ \end{gathered}

x

2

−12x+8x−96=0

\begin{gathered}\rm \: x(x - 12) + 8(x - 12) = 0 \\ \end{gathered}

x(x−12)+8(x−12)=0

\begin{gathered}\rm \: (x - 12)(x + 8) = 0 \\ \end{gathered}

(x−12)(x+8)=0

\begin{gathered}\rm\implies \:x = 12 \: \: or \: \: x = - 8 \: \{rejected \} \\ \end{gathered}

⟹x=12orx=−8{rejected}

So, Shoba bought 12 pens for Rs 48

\rule{190pt}{2pt}

Additional information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac

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