Question

If a boy sells a book for rupees 450, he makes a loss of 10%. To gain 10%, what should be the selling price?

Answer 1

${\underline {\boxed {\Large {\bf \gray { \odot \: Rs \: 550} }}}}$

Given:

$\odot$ SP of the book = Rs. 450

$\odot$ Loss % he got = 10%

To calculate:

$\odot$ To gain 10%, what should be the selling price?

Calculation:

Let us calculate the CP at Rs 450 & a loss of 10% first.

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As we know that,

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$\star$ $\boxed{\sf \purple { CP = \dfrac{100}{100-Loss \: \%} \times SP } }$

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Where,

• $\bf { Loss \: \% = 10 \: \% }$
• $\bf { SP = Rs \: 450 }$

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$\odot\underline{ \boldsymbol{According \: to \: the \: question}}$

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Step 1 : Substituting values.

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$\sf{ \dashrightarrow CP =Rs \left ( \dfrac{100}{100-10\%} \times 450 \right ) }$

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Step 2 : Performing substraction.

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$\sf{ \dashrightarrow CP =Rs \left ( \dfrac{100}{90} \times 450 \right ) }$

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Step 3 : Cancelling 90 and 450 in denominator and numerator by 90.

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$\sf{ \dashrightarrow CP =Rs (100 \times 5) }$

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Step 4 : Performing multiplication.

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$\boxed{ \sf{ \dashrightarrow CP =Rs \: 500 }}$$\red{\bigstar }$

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Now, we have :

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• $\bf { Desired \: gain \: \% = 10 \: \% }$
• $\bf { CP = Rs \: 500 }$
• $\bf { Desired \: SP = ? }$

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Step 5 : Reviewing formula.

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$\star$ $\boxed{\sf \purple { SP = \dfrac{100+Gain\: \%}{100} \times CP } }$

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Step 6 : Substituting values.

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$\sf {Desired \: SP = \dfrac{100+10 \%}{100} \times 500}$

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Step 6 : Performing addition.

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$\sf {Desired \: SP = \Bigg ( \dfrac{110}{100} \times 500 \Bigg ) }$

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Step 7 : Cancelling denominator and numerator by 100.

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$\sf {Desired \: SP = Rs (110 \times 5)}$

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Step 8 : Performing multiplication.

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$\boxed{ \sf{ \dashrightarrow Desired \: SP =Rs \: 550 }}$$\red{\bigstar }$

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Hence, to gain 10%, Rs 550 should be the selling price