Multiple choice

Emily, the owner of a beloved food truck, eagerly joined a local food festival. She purchased a variety of food items from suppliers for a total of Rs. 6,080. Each food item had the same cost price. Emily decided to sell some items at a 30% profit, while the rest, 20 items in total, at a 15% loss. Her aim was to make a profit of Rs. 1,536. Due to the festival's popularity, Emily sold 15 more items than planned at the profit margin and the rest at a loss. In the end, she made an overall profit of Rs. 1,752. What was the cost price of each food item, in rupees?

  1. 29

  2. 30

  3. 31

  4. 32

  5. 33
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the cost price per item and n be the total number of items. Total cost = nx = 6080. The first scenario gives 0.3(n-20)x - 0.15(20)x = 1536. The second scenario gives 0.3(n-5)x - 0.15(5)x = 1752. Solving these equations leads to x = 32.

AI explanation

Emily bought items for Rs. 6,080, and selling 15 more items at a 30% profit increased her overall profit from Rs. 1,536 to Rs. 1,752, a difference of Rs. 216. Since the extra 15 items yielded Rs. 216 in profit at 30%, the profit per item is 216 divided by 15, which is Rs. 14.4. This 30% profit means the cost price of each item is 14.4 divided by 0.3, resulting in Rs. 32.

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