Question

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Q.1. A shopkeeper bought two TV sets ₹10.000 each.
He sold one at a profit of 10% and the other at a loss of 10%. Find whether he made an overall profit or loss.​

Answer 1

$\huge{\underline{\underline{\sf{\purple{Required\:Answer:}}}}}$

Combined CP of two TV sets

$\displaystyle{\sf{\:\:\:\:\:\:\:\:\:\:= 2 \times ₹ 10,000 = ₹20,000}}$

$\large{\bf{For\:1^{st}\:TV}}$

$\displaystyle{\sf{\:\:\:\:\:C.P.\:=\: ₹10,000}}$

$\displaystyle{\sf{\:\:Profit\:rate\:=10\%}}$

$\displaystyle{\sf{ \therefore\:\:\:\:Profit\:=\:10\% \:of\:₹10,000}}$

$\displaystyle{\sf{ \:\:\:\:\:\:\:\:\:= \dfrac{10}{100} \times 10000 = ₹1000}}$

$\displaystyle{\sf{\therefore\:\:\:\:\:S.P. = C.P. + Profit}}$

$\displaystyle{\sf{\:\:\:\:\:\:\:\:\:\:=₹10,000 + ₹1,000}}$

$\displaystyle{\sf{\:\:\:\:\:\:\:\:\:\:=₹11,000}}$

$\large{\bf{For\:2^{nd}\:TV}}$

$\displaystyle{\sf{\:\:\:\:\:C.P.\:=\: ₹10,000}}$

$\displaystyle{\sf{\:\:Loss\:rate\:=10\%}}$

$\displaystyle{\sf{ \therefore\:\:\:\:Loss\:=\:10\% \:of\:₹10,000}}$

$\displaystyle{\sf{ \:\:\:\:\:\:\:\:\:= \dfrac{10}{100} \times 10000 = ₹1000}}$

$\displaystyle{\sf{\therefore\:\:\:\:\:S.P. = C.P. - Loss}}$

$\displaystyle{\sf{\:\:\:\:\:\:\:\:\:\:=₹10,000 - ₹1,000}}$

$\displaystyle{\sf{\:\:\:\:\:\:\:\:\:\:=₹9000}}$

$\displaystyle{\sf{\therefore \:\:Combined\:SP\:of\:two\:TV\:sets}}$

$\displaystyle{\sf{\:\:\:\:\:\:=₹11000 + ₹9000 = ₹20000}}$

$\displaystyle{\sf{\because\:\:\:\:Combined\:CP\:=\:Combined\:SP}}$

$\large{\boxed{\sf{\red{ \therefore\:\:He\:made\:no\:overall\:profit\:or\:loss.}}}}$

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Answer 2

∴ There is no overall profit or loss. A shopkeeper bought two TV sets at Rs 10,000 each. He sold one at a profit 10% and the other at a loss of 10%.