Question

The cost price of a coat is 600. It was sold at a profit of 5%. Find the selling price of the coat.

Answer 1

$\bf \underline{\underline{Given}}$

$\sf The \: cost \: price \: of \: a \: coat \: is \: Rs. \: 600$

$\bf \underline{\underline{To \: find}}$

$\sf Find \: its \: selling \: price \: it \: is \: sold \: at \: 5 \: profit.$

$\bf \underline{\underline{Solution}}$

$\sf If \: cost \: price \: and \: gain \: \% \: is \: given \: then,$

$\sf Selling \: price = \dfrac{(100 + Gain\:\% ) }{100} \times Cost \: price$

$\bf \: \quad\quad\quad\quad\quad\quad\quad\quad \underline{ \red{OR }}$

$\sf Selling \: price = \bigg(1 + \dfrac{Gain\:\%}{100} \bigg) \: of \: Cost \: price$

$\bf \underline{Now},$

$\sf \underline{Substituting \: the \: values},$

$\sf Selling \: price = \dfrac{(100 + 5) }{100} \times 600$

$\sf \implies \dfrac{105 }{100} \times 600$

$\sf \underline{Simplifying \: the \: above \: expression },$

$\sf \implies \dfrac{105 }{1\!\!\!\not0\!\!\!\not0} \times 6\!\!\!\not0\!\!\!\not0$

$\sf \implies 105 \times 6$

$\sf \implies Rs. \: 630$

$\underline{ \boxed{ \red{\bf Hence, Selling \: price = Rs. \: 630 }}}$

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$\sf\: MORE\: TO \: KNOW \: :$

$\begin{gathered} \small\boxed{\begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P\: -\: C.P} \\ \\ \bigstar \:\sf{Loss = C.P \: -\: S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\:\%}{100} \times C.P} \\ \\ \bigstar \: \sf{C.P =\dfrac{100}{100+Gain\:\%} \times S.P} \\ \\\bigstar \: \sf{S.P = \dfrac{100-loss\:\%}{100} \times C.P} \\ \\ \bigstar \: \sf{C.P =\dfrac{100}{100-loss\:\%} \times S.P}\end{array}}\end{gathered}$

Answer 2

Given:

• Cost price of a coat (CP) = ₹600
• Profit on coat = 5%

To Find:

• Selling price of coat (SP)?

Solution:

Here, given that CP of a coat is ₹600 and that coat is sold at 5% profit.

According to find SP of coat ,

We know that:

• $\large{\boxed{\underline{\bf{SP~=~\bigg(\dfrac{100+gain\%}{100}\bigg)×CP}}}}$

Therefore,

$\large{\sf{SP~=~\bigg(\dfrac{100+gain\%}{100}\bigg)×CP}}$

$\implies\large{\sf{SP~=~\bigg(\dfrac{100+5}{100}\bigg)×600}}$

$\implies\large{\sf{SP~=~\bigg(\dfrac{105}{100}\bigg)×600}}$

$\implies\large{\sf{SP=\bigg(\dfrac{105}{\cancel{100}}\bigg)×\cancel{600}}}$

$\implies\large{\sf{SP~=~ 105×6}}$

$\implies\large{\sf{SP~=~ 630}}$

Therefore,

• SP of coat = ₹630