Multiple choice

The total cost of a stove with cooker was Rs. 13,125. The cooker was sold at a profit of 30% and the stove at a loss of 20%. If the sale price was the same for both the items, then the cost price of the cheaper item of the two was

  1. Rs. 8125

  2. Rs. 5000

  3. Rs. 6562.5

  4. Rs. 6175
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C1 and C2 be costs. C1(1.3) = C2(0.8) = S. C1+C2 = 13125. C2 = 1.3/0.8 * C1 = 1.625 * C1. C1 + 1.625 * C1 = 13125 => 2.625 * C1 = 13125 => C1 = 5000. C2 = 8125. The cheaper item is 5000.

AI explanation

Let the cost price of the stove be x and the cooker be (13125 minus x), and set their sale prices equal using the equation 0.8x equals 1.3(13125 minus x). Solving this equation gives 0.8x equals 17062.5 minus 1.3x, so 2.1x equals 17062.5, making the cost price of the stove Rs. 8125. The cost price of the cooker is 13125 minus 8125, which equals Rs. 5000, making the cooker the cheaper item.

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