Directions: Two quantities, labeled Quantity I and Quantity II, are provided below. Determine the relationship between the two quantities and choose the appropriate option.

Quantity I: A retailer marks up a smart speaker by 50% over its cost price. After offering a 20% discount on the marked price, the retailer earns a profit of $40. Find the cost price of the smart speaker.

Quantity II: A trader buys 30 units of electronic gadgets at $40 each and sells them for $55 each. If he incurs a transportation expenditure of $150, calculate his net profit.

Correct Answer: Quantity I < Quantity II

To determine the relationship between Quantity I and Quantity II, we will calculate the numerical value of each quantity step-by-step.

Step 1: Calculate Quantity I

Let the cost price of the smart speaker be $C$.

The retailer marks up the price by 50% over its cost price:

$\text{Marked Price (MP)}=C+0.50C=1.50C$

Next, a 20% discount is offered on the marked price:

$\text{Discount}=0.20\times 1.50C=0.30C$

The selling price (SP) after applying the discount is:

The profit earned is the difference between the selling price and the cost price, which is given as $40:

$\text{Profit}=\text{Selling Price}-\text{Cost Price}$

$40=1.20C-C$

$40=0.20C$

$C=\frac{40}{0.20}=200$

Therefore, Quantity I (Cost Price) = $200.

Step 2: Calculate Quantity II

The trader buys 30 units of electronic gadgets at $40 each:

$\text{Purchase Cost}=30\times 40=1200$

Including the transportation cost of $150, the total expenditure (total cost price) is:

$\text{Total Cost Price}=1200+150=1350$

The trader sells all 30 units at $55 each:

$\text{Total Selling Price}=30\times 55=1650$

Now, calculate the net profit:

$\text{Net Profit}=\text{Total Selling Price}-\text{Total Cost Price}$

$\text{Net Profit}=1650-1350=300$

Therefore, Quantity II (Net Profit) = $300.

Step 3: Compare Quantity I and Quantity II

Comparing the two obtained values:

Quantity I = $200

Quantity II = $300

Since $200 < $300, Quantity I < Quantity II.

Conclusion:

The correct relationship is Quantity I < Quantity II.