Question

Rita sold two printers for Rs 2100 each. On one of the printers she made a

profit of 20% and on the other she incurred a loss of 20%.Find the total loss or

gain and the net loss or gain percentage.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Net\:loss\%=4\%}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given : }} \\ \tt: \implies Selling \: price \: of \:two \: printer = 2100 \: each \\ \\ \tt: \implies Profit\% = 20\% \: on \: one \: printer \\ \\ \tt: \implies Loss\% = 20\% \: on \: other \: printer \\ \\ \red{\underline \bold{To \: Find : }} \\ \tt: \implies Net \: loss\% \: or \: gain\% = ?$

• According to given question :

$\text{Let \: C.P \: be \: x} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Selling \: price = Cost \: price + Profit\% \: of \: cost \: price \\ \\ \tt: \implies 2100 = x + 20\% \: of \: x \\ \\ \tt: \implies 2100 = x + \frac{20}{100} x \\ \\ \tt: \implies 2100 = x + 0.2x \\ \\ \tt: \implies 2100 = 1.2x \\ \\ \tt: \implies x = \frac{2100}{1.2} \\ \\ \green{\tt: \implies x = 1750} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Profit = S.P - C.P \\ \\ \tt: \implies Profit = 2100 - 1750 \\ \\ \tt: \implies Profit = 350 \\ \\ \text{Let \: C.P \: of \: another \: printer \: be \: y} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Selling \: price = Cost \: price - 20\% \: of \: Cost \: price \\ \\ \tt: \implies 2100 = y - 0.2y$

$\tt: \implies 2100 = 0.8y \\ \\ \tt: \implies y = \frac{2100}{0.8} \\ \\ \green{\tt: \implies y = 2625} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Loss =C.P - S.P \\ \\ \tt: \implies loss = 2625 - 2100 \\ \\ \green{ \tt: \implies Loss = 525} \\ \\ \bold{For \: net \: profit \: or \: Loss} \\ \tt: \implies Net \: Loss = 525 - 350 \\ \\ \green{\tt: \implies Net \: Loss = 175 \: rupees} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Net\:Loss\% = \frac{Loss}{Total \: C.P} \times 100 \\ \\ \tt: \implies Net\: Loss\% = \frac{175}{4375} \times 100 \\ \\ \tt: \implies Net\: Loss\% =0.04 \times 100 \\ \\ \green{\tt: \implies Net\: Loss\% =4\%}$

Answer 2

$</p><p>\tt{\huge{\pink{Hello!!! }}}$

The Question is solved Elaborately in the above Answer.

Hence, in my answer, I am going to mention a Shortcut Formula To Solve This Type Of Questions.

$</p><p>\tt{\red{Given \: - }}$

Profit 1 = Loss 2 = 20%

Suppose for any two objects sold someone gains n% on the first sale and looses n% on the second sale :

Net loss = $\tt{\orange{\implies{\dfrac{{n}^2}{100} \% }}}$

Hence, For This Case,

$</p><p>\tt{\purple{Net \: Loss \: Percentage \: =\dfrac{{n}^2}{100} \% = \dfrac{400}{100} \% = 4\% }} ........ (A)$