Question

Mr. Sen sells 8 articles for Rs. 36 and makes a profit of 20% . Find his gain or loss percent of he sell 16 such articles for Rs. 54.
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Answer 1

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

Given that,

• Selling Price of 8 articles = Rs 36

• Profit % = 20 %

We know that,

$\red{\rm :\longmapsto\:\boxed{\sf{ \: \: \: Cost \: Price = \frac{100 \times Selling \: Price}{100 + Profit\%} \: \: \: }}}$

So, on substituting the values, we get

$\rm :\longmapsto\:Cost \: Price \: = \: \dfrac{100 \times 36}{100 + 20}$

$\rm :\longmapsto\:Cost \: Price \: = \: \dfrac{3600}{120}$

$\bf\implies \:Cost \: Price = 30$

So, Cost price of 8 articles = Rs 30

Now, we have,

Cost Price of 16 articles = Rs 60

Selling Price of 16 articles = Rs 54

➢ This implies, Selling Price < Cost Price

➢ It means, there is Loss in this transaction.

➢ Loss = Cost Price - Selling Price = 60 - 54 = Rs 6

We know,

$\red{\rm :\longmapsto\:\boxed{\tt{ \: \: Loss \: \% \: = \: \frac{Loss}{Cost \: Price} \: \times \: 100 \: \% \: \: }}}$

So, on substituting the values, we get

$\rm :\longmapsto\:Loss \: \% \: = \: \dfrac{6}{60} \times 100\%$

$\rm\implies \:\boxed{\tt{ \: \: Loss \: \% \: = \: 10 \: \% \: \: }}$

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$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$