Multiple choice

Rahul bought two cycles for a total sum of Rs. 1,500. He sold one cycle at 20% loss and the other cycle at 20% gain. If the selling price of both the cycles is the same, find the cost price of each of the two cycles.

  1. Rs. 500, Rs. 1,000

  2. Rs. 600, Rs. 900

  3. Rs. 750 each

  4. Rs. 550, Rs. 950
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP1 and CP2 be the costs. CP1 + CP2 = 1500. SP1 = 0.8 * CP1. SP2 = 1.2 * CP2. 0.8 * CP1 = 1.2 * CP2 => CP1 = 1.5 * CP2. 1.5 * CP2 + CP2 = 1500 => 2.5 * CP2 = 1500 => CP2 = 600. CP1 = 900.

AI explanation

When two items are sold at the same selling price and one is sold at a 20% loss while the other is sold at a 20% gain, use the proportion method to find their cost prices. The cost price of the first cycle to the second cycle is inversely proportional to their selling percentages, meaning CP1 divided by CP2 equals 120 divided by 80, simplifying to a 3:2 ratio. Given that the total cost is Rs. 1500, the individual cost prices are calculated by dividing 1500 by 5 parts, giving Rs. 300 per part. Multiplying by the ratio values, the cost prices are Rs. 900 and Rs. 600.

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