A man purchases two table lamps for rs 2430 By selling one table lamp at a profit of 6% - Maths - Comparing Quantities

Question

A man purchases two table lamps for rs 2430 By selling one table
lamp at a profit of 6% and the other at a loss of 3% he neither
gains nor losses on this transaction Find the cost price of each
lamp

Manbar Singh · Accepted Answer

Let the CP of first table lamp = Rs xThen the CP of second table lamp = Rs2430 - xProfit on selling first lamp = 6%Profit % = ProfitCP×100%⇒6 = Profitx×100⇒50profit = 3x⇒50SP-CP = 3x⇒50SP - x = 3x⇒SP = Rs53x50Loss on selling second lamp = 3%loss % = lossCP×100%⇒3 = loss2430-x×100⇒100 loss = 7290 - 3x⇒100CP - SP = 7290-3x⇒1002430-x-SP = 7290-3x⇒SP = Rs235710-97x100Total SP of both lamps = 53x50 + 235710-97x100 = Rs9x+235710100Total CP of both lamps = Rs 2430Since there is neither gain nor loss inthe transaction, soTotal SP of both lamps = Total CP of both lamps⇒9x+235710100 = 2430⇒9x + 235710 = 243000⇒9x = 7290⇒x = 810So, CP of first lamp = Rs 810CP of second lamp = 2430 - 810 = Rs 1620

A man purchases two table lamps for rs 2430. By selling one table lamp at a profit of 6% and the other at a loss of 3% he neither gains nor losses on this transaction . Find the cost price of each lamp