Question

A certain manufacturer sells an item to the whole seller at a profit of \(20\%\) of the cost price. The whole seller sells the item further to the retailer at a profit of \(20\%\) of his cost price. If the retailer sells the item further to the consumer at a profit of \(20\%\), then the buying price for the consumer is what percentage above the cost price of the manufacturer?

• A. 60
• B. 62.8
• C. 68.2
• D. 72.8

Answer 1

The Correct Option is D

Step 1: Let the cost price of the manufacturer be \( C \). 

Step 2: The manufacturer sells the item to the wholesaler at a 20% profit:

\[ \text{Wholesaler's Cost} = C + 0.2C = 1.2C \]

Step 3: The wholesaler sells the item to the retailer at a 20% profit:

\[ \text{Retailer's Cost} = 1.2C \times 1.2 = 1.44C \]

Step 4: The retailer sells the item to the consumer at a 20% profit:

\[ \text{Consumer's Cost} = 1.44C \times 1.2 = 1.728C \]

Step 5: The percentage increase in price from manufacturer to consumer:

\[ \frac{(1.728C - C)}{C} \times 100 = 72.8\% \]

Final Answer:

The price increased by 72.8%.