Question

A man purchases two table lamps for rs 2430 . By selling one table lamps at a profit of 6 per cent and the other at a loss of 3 per cent , he neither gains or loss on this transaction. find the cost price of each table lamp.​

Answer 1

${ \bold{ \huge{ \red{ \underline{ \purple{question}}}}}}$

A man purchases two table lamps for Rs. 2430. By selling one table lamp at a profit of 6 percent and the other at a loss of 3 percent, he neither gains or loss on his transaction. Find the cost price of each table lamp.

${ \bold{ \huge{ \red{ \underline{ \purple{solution}}}}}}$

${ \bold{ \blue{ given}}}$

• Total cost price of the 2 table lamps = Rs. 2430

• gain on table lamp 1 = 6%

• loss on table lamp 2 = 3%

${ \bold{ \blue{to \: find}}}$

• Cost price of each table lamp???

Let the cost price of table lamp 1 be Rs. x

cost price of ( lamp 1 + lamp 2 ) = Rs. 2430

cost price of lamp 2 = Rs. ( 2430 - x )

${ \bold{ \underline{ table \: lamp \: 1 \: }}}$

• cost price ( C.P. ) = Rs. x

• gain = 6 %

• selling price ( S.P. )

${ \boxed{ \bold{ \red{s.p. = \frac{c.p.}{100} \times (100 + gain \: prcnt)}}}}$

${ \bold{ \implies{s.p. = \frac{x}{100} \times (100 + 6)}}}$

${ \bold{ \implies{s.p. = rs. \: \frac{106x}{100} }}}$

${ \bold{ \underline{table \: lamp \: 2 \: }}}$

• Cost price ( C.P. ). = Rs. ( 2430 - x )

•. loss = 3%

• selling price ( S.P. )

${ \boxed{ \bold{ \red{ s.p. = \frac{c.p.}{100 } \times (100 - loss \: prcnt)}}}}$

${ \bold{ \implies{s.p. = \frac{(2430 - x)}{100} \times (100 - 3)}}}$

${ \bold{ \implies{s.p. = \: rs. \: \frac{(2430 - x) \times 97}{100} }}}$

• since,. it's given that he neither gains or loss in his transaction

therefore,

Total cost price =. total selling price

total selling price = Rs. 2430

Total selling price = S.P. of ( lamp 1 + lamp 2 )

${ \bold{2430 = \frac{106x}{100} + \frac{(2430 - x)97}{100}}}$

${ \bold{ \implies{2430 = \frac{106x + (2430 \times 97) - 97x}{100}}}}$

${ \bold{ \implies{243000 = (106x - 97x) + 235710}}}$

${ \bold{ \implies{9x + 235710 = 243000}}}$

${ \bold{ \implies{9x = 243000 - 235710}}}$

243

${ \bold{ \implies{9x = 7290}}}$

${ \bold{ \implies{x = 810}}}$

therefore,

• Cost price of lamp 1 = Rs. x = Rs. 810

• Cost price of lamp 2= 2430 - 810 = Rs. 1620

Answer 2

Step-by-step explanation:

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