Multiple choice

Two musical instruments were purchased for Rs. 8,000. The first was sold at a profit of 40% and the second at a loss of 40%. If the sale price was the same in both cases, then the cost price of the cheaper instrument (in Rs.) was:

  1. 2500

  2. 2400

  3. 2200

  4. 2000

  5. 2300
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP1 and CP2 be costs. SP1 = 1.4 * CP1, SP2 = 0.6 * CP2. Given 1.4 * CP1 = 0.6 * CP2, so CP2 = (1.4/0.6) * CP1 = (7/3) * CP1. CP1 + CP2 = 8000 => CP1 + (7/3)CP1 = 8000 => (10/3)CP1 = 8000 => CP1 = 2400. CP2 = 5600. Cheaper is 2400.

AI explanation

When two items are sold at the same price but one at a profit of p% and the other at a loss of p%, there is always an overall loss. However, we can equate the sale prices: 1.40 times the cost price of the first equals 0.60 times the cost price of the second, giving a cost price ratio of 3 to 7. With the total cost being Rs. 8,000, the cost price of the cheaper instrument is 3/10 of 8,000, which equals Rs. 2,400.

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