Question

A fruit seller makes a profit of 20%
by selling oranges at a certain
price. If he charges 1.2 higher per
orange he would gain 40%. Find the
original price at which he sold an
orange.​

Answer 1

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

☆ Let Cost Price of orange be Rs x

Case :- 1

Cost Price of orange = Rs x

Profit % = 20 %

Now, We evaluate the Selling price of an orange when profit is 20 %.

We know,

$\rm :\longmapsto\:Selling \: Price = \dfrac{(100 + Profit\%)}{100} \times Cost \: Price$

$\rm :\longmapsto\:Selling \: Price = \dfrac{(100 + 20)}{100} \times \: x$

$\rm :\longmapsto\:Selling \: Price = \dfrac{120}{100}x$

$\bf :\longmapsto\:Selling \: Price = \dfrac{6}{5}x - - - (1)$

Case :- 2

Cost Price of orange = Rs x

Profit % = 40 %

Now, we evaluate the Selling price of an orange when Profit is 40 %.

We know,

$\rm :\longmapsto\:Selling \: Price = \dfrac{(100 + Profit\%)}{100} \times Cost \: Price$

$\rm :\longmapsto\:Selling \: Price = \dfrac{(100 + 40)}{100} \times \: x$

$\rm :\longmapsto\:Selling \: Price = \dfrac{(140)}{100} \times \: x$

$\bf :\longmapsto\:Selling \: Price = \dfrac{(7)}{5} x$

According to statement,

$\rm :\longmapsto\:\dfrac{7x}{5} - \dfrac{6x}{5} = 1.2$

$\rm :\longmapsto\:\dfrac{7x - 6x}{5} = 1.2$

$\rm :\longmapsto\:\dfrac{x}{5} = 1.2$

$\bf\implies \:x = 6$

☆ On substituting the value of x, in equation (1), we get

$\bf :\longmapsto\:Selling \: Price = \dfrac{6}{5} \times 6 = 7.2$

Hence,

$\: \: \: \: \: \: \: \underbrace{ \boxed{ \bf \: Selling \: Price \: of \: orange \: is \: Rs \: 7.20}}$

Additional Information :-

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