Question

A shopkeeper bought two tv sets for Rs. 10,000 each. he sold one at a profit of 8% and other at a loss of 10% . find the overall loss or profit​

Answer 1

$\underline{\underline{\sf{\maltese\:\:Given}}}$

$\sf \Rrightarrow \: A \: shopkeeper \: bought \: two \: T.V \: sets \: for \: Rs. \: 10000 \: each.$

$\sf \Rrightarrow \: He \: sold \: one \: at \: a \: profit \: of \: 8\% \: and \: other \: at \: a \: loss \: of \: 10 \%$

$\underline{\underline{\sf{\maltese\:\:To \: find}}}$

$\implies \sf Overall \: loss \: or \: profit = \: ?$

$\underline{\underline{\sf{\maltese\:\: Solution}}}$

$\sf \implies Cost \: price \: of \: first \: T.V = Rs. \: 10000$

$\sf \implies Profit = 8 \%$

$\sf \implies SP \: = \: \cfrac{100 + P}{100} \: \times \: CP$

$\sf \implies SP \: = \: \cfrac{100 + 8}{100} \: \times \: 10000$

$\sf \implies SP \: = \: \cfrac{108}{ \cancel{100}} \: \times \: \cancel{10000}$

$\sf \implies SP \: = \: 108 \times 100$

$\sf \implies SP \: = Rs. \: 10800$

$\underline {\sf \therefore \: Selling \: price \: of \: first \: T.V = Rs. \: 10800}$

$\quad$

$\sf \implies Cost \: price \: of \: second \: T.V = Rs. \: 10000$

$\sf \implies Loss = 10\%$

$\sf \implies SP \: = \: \cfrac{100 - L }{100} \: \times \: CP$

$\sf \implies SP \: = \: \cfrac{100 -10 }{100} \: \times \: 10000$

$\sf \implies SP \: = \: \cfrac{90 }{ \cancel{100}} \: \times \: \cancel{10000}$

$\sf \implies SP \: = \: 90 \times 100$

$\sf \implies SP \: = Rs. \: 9000$

$\underline {\sf \therefore \: Selling \: price \: of \: second \: T.V = Rs. \: 9000}$

$\quad$

$\small{ \bf Now},$

$\sf \implies Total \: cost \: price = Rs. \: (10000+10000)$

$\sf \implies \boxed{ \sf Total \: cost \: price = Rs. \: 20000} \: \: \bigstar$

$\sf \implies Total \: selling \: price = Rs. \: (10800+9000)$

$\sf \implies \boxed{\sf Total \: selling \: price = Rs. \: 19800} \: \: \bigstar$

$\small{ \bf So},$

$\sf \implies Rs. \: 20000 \: > \: Rs. \: 19800$

$\small{ \bf Hence},$

$\sf \implies Cost \: price \: > \: Selling \: price\:\:\:\:\bf [Loss]$

$\small{ \bf Now},$

$\sf \implies Overall \: loss = Cost \: price - Selling \: price$

$\sf \implies Overall \: loss = Rs. \: (10800-9000)$

$\sf \implies Overall \: loss = Rs. \: 200$

$\small{ \bf Therefore},$

$\sf \implies \underline{\boxed{\sf Overall \: loss = Rs. \: 200}}\: \: \bigstar$