Question

Ganesh sells two chairs for Rs. 800 each, gains 20% on one and lose 20% on the other. Find his gain or lose percentage in the entire transaction?

Answer 1

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

Given that

• Ganesh sells two chairs for Rs. 800 each, gains 20% on one chair and lose 20% on the other chair.

Consider Case - 1

Given that

• Selling Price of chair = Rs 800

• Gain % = 20 %

Let assume that

• Cost Price of chair be Rs x

We know,

$\rm :\longmapsto\:\boxed{ \tt{ \: CP = \frac{100 \times SP}{100 + gain \: \% \: } }}$

So, on substituting the values, we get

$\rm :\longmapsto\:x = \dfrac{100 \times 800}{100 + 20}$

$\rm :\longmapsto\:x = \dfrac{80000}{120}$

$\rm \implies\:\boxed{ \tt{ \: x \: = \: 666.67 \: }}$

Consider Case - 2

Given that

• Selling Price of chair = Rs 800

• Loss % = 20 %

Let assume that

• Cost Price of chair be Rs y

We know that

$\rm :\longmapsto\:\boxed{ \tt{ \: CP = \frac{100 \times SP}{100 - loss \: \% \: } }}$

So, on substituting the values, we get

$\rm :\longmapsto\:y = \dfrac{100 \times 800}{100 - 20}$

$\rm :\longmapsto\:y = \dfrac{80000}{80}$

$\rm \implies\:\boxed{ \tt{ \: y \: = \: 1000 \: }}$

So, in the whole transaction, we have

Selling price of 2 chairs = 800 + 800 = Rs 1600

Cost Price of 2 chairs = 666.67 + 1000 = Rs 1666.67

$\rm \implies\:CP > SP$

$\rm \implies\:Loss \: in \: the \: transaction$

and we know

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Loss\% = \frac{CP - SP}{CP} \times 100\% \: }}}$

$\rm :\longmapsto\:Loss\% = \dfrac{1666.67 - 1600}{1666.67} \times 100\%$

$\rm :\longmapsto\:Loss\% = \dfrac{66.67}{1666.67} \times 100\%$

$\rm :\longmapsto\:\boxed{ \tt{ \: Loss\% = 4.0002 \: \approx \: 4\% \: }}$

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

Answer 2

Answer:

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