Multiple choice

A dealer sold a VCR and a TV for $Rs.38560$ making profit of $12$% on VCR and $15$% on TV. By selling them for $Rs.38620$, he would have realised a profit of $15$% on VCR and $12$% on TV. Find the cost price of each

  1. CP of VCR $=Rs.15000$ and CP of TV $=Rs.17000$
  2. CP of VCR $=Rs.21000$ and CP of TV $=Rs.32000$
  3. CP of VCR $=Rs.18000$ and CP of TV $=Rs.16000$
  4. CP of VCR $=Rs.12000$ and CP of TV $=Rs.15000$
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C Correct answer
Explanation

Let V = CP of VCR, T = CP of TV. 1.12V + 1.15T = 38560. 1.15V + 1.12T = 38620. Adding: 2.27(V+T) = 77180 => V+T = 34000. Subtracting: 0.03V - 0.03T = 60 => V-T = 2000. 2V = 36000 => V = 18000, T = 16000.

AI explanation

Let the cost price of the VCR be x and the TV be y; the first scenario gives 1.12x + 1.15y = 38560, and the second gives 1.15x + 1.12y = 38620. Subtracting the first equation from the second yields 0.03x - 0.03y = 60, meaning x - y = 2000. Substituting y = x - 2000 into the first equation provides 1.12x + 1.12x - 2240 = 38560, so 2.24x = 40800, yielding the VCR cost price of Rs. 18000 and the TV cost price of Rs. 16000.

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