Question

A shopkeeper sold two fan at rupees 1980 each on one he gains 10% find and other he lost 10% calculate the gain or loss percent on the whole transaction​

Answer 1

Answer:

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Answer 2

Solution :

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

A shopkeeper sold two fan at Rs.1980 each on one he gains 10% and other he lost 10%.

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

The gain or loss percent on the whole transaction.

$\bf{\underline{\bf{Explanation\::}}}}$

Let the 1st fan of Cost price be Rs.R

Let the 2nd fan of Cost price be Rs.M

$\bf{\large{\underline{\tt{1st\:case\::}}}}$

$\bf{We\:have}\begin{cases}\sf{Cost\:price\:(C.P.)_1=Rs.R}\\ \sf{Selling\:price\:(S.P.)=Rs.1980}\\ \sf{Gain\:(\%)=10\% \end{cases}}$

Therefore;

$\mapsto\sf{Gain\%=\bigg(\dfrac{S.P._1-C.P._1}{C.P._1} \bigg)\times 100\%}\\\\\\\mapsto\sf{\cancel{10}\%=\bigg(\dfrac{1980-R}{R} \bigg)\times 10\cancel{0}\%}\\\\\\\mapsto\sf{\%=\dfrac{19800-10R}{R} }\\\\\\\mapsto\sf{R=19800-10R}\\\\\\\mapsto\sf{R+10R=19800}\\\\\\\mapsto\sf{11R=19800}\\\\\\\mapsto\sf{R=\cancel{\dfrac{19800}{11} }}\\\\\\\mapsto\sf{\red{R=Rs.1800}}$

$\bf{\large{\underline{\tt{2nd\:case\::}}}}$

$\bf{We\:have}\begin{cases}\sf{Cost\:price\:(C.P.)_2=Rs.M}\\ \sf{Selling\:price\:(S.P.)=Rs.1980}\\ \sf{Loss\:(\%)=10\% \end{cases}}$

Therefore;

$\mapsto\sf{Loss\%=\bigg(\dfrac{C.P._2-S.P._2}{C.P._2} \bigg)\times 100\%}\\\\\\\mapsto\sf{\cancel{10}\%=\bigg(\dfrac{M-1980}{M} \bigg)\times 10\cancel{0}\%}\\\\\\\mapsto\sf{\%=\dfrac{10M-19800}{M} }\\\\\\\mapsto\sf{M=10M-19800}\\\\\\\mapsto\sf{M-10M=-19800}\\\\\\\mapsto\sf{-9M=-19800}\\\\\\\mapsto\sf{M=\cancel{\dfrac{-19800}{-9} }}\\\\\\\mapsto\sf{\red{M=Rs.2200}}$

Thus;

Total Cost price of both fan = R + M = Rs.(1800+2200) = Rs.4000

Total Selling price of both fan = Rs.3960

A/q

C.P. > S.P.

$\mapsto\sf{Loss\%=\bigg(\dfrac{C.P.-S.P.}{C.P.}\bigg) \times 100\%}\\\\\\\mapsto\sf{Loss\%=\bigg(\dfrac{4000-3960}{4000} \bigg)\times 100\%}\\\\\\\mapsto\sf{Loss\%=\dfrac{40}{40\cancel{00}} \times \cancel{100}\%}\\\\\\\mapsto\sf{Loss\%=\cancel\bigg({\dfrac{40}{40} \bigg)}\%}\\\\\\\mapsto\sf{\red{Loss\%=1\%}}$

Thus;

$\underline{\sf{The\:loss\:percent\:on\:the\:whole\:transaction\:is\:1\%}}}$