AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 4 Medium

A certain product is originally sold at its regular price, with a profit of 20\% of the cost per unit. Later, it is sold at 90\% of the original price, and the total profit increases by 20\% compared to before. What is the multiple of the new sales volume compared to the original sales volume?

  • A.

    2

  • B.

    2.5

  • C.

    3

  • D.

    3.5

  • E.

    4

Answer:C

Assume the cost price is 100 dollars. If the product is sold at the original price for 10 units, then the original selling price is: 100 \times (1 + 20\%) = 120 \text{ (dollars)}

The discounted price is: 120 \times 90\% = 108 \text{ (dollars)}

The total profit from selling 10 units at the original price is: (120 - 100) \times 10 = 200 \text{ dollars}

After the price reduction, the total profit increases by 20\%, so the new total profit is: 200 \times (1 + 20\%) = 240 \text{ dollars}

The number of units sold after the price reduction is: 240 \div (108 - 100) = 30 \text{ units}

Therefore, the new sales volume is: 30 \div 10 = 3 \text{ times the original}

So the answer is \text{D}.

Related Problems
Problem 2 AMC 8 Daily Practice Round 8
Problem 3 AMC 8 Daily Practice Round 8
Problem 5 AMC 8 Daily Practice Round 8
Problem 6 AMC 8 Daily Practice Round 8
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