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Difficulty: HardProfit and Loss

An electronics restorer buys a bulk lot of 4040 tablets for $120\$120 each. The restorer spends an additional $1,200\$1,200 total for replacement parts to repair them. Unfortunately, 1010 of the tablets are too severely damaged to repair and must be discarded. If the restorer wants to make exactly a 25%25\% profit on the total investment, what must be the selling price for each of the remaining functional tablets?

  1. $250\$250Answer
  2. B
    $200\$200
  3. C
    $187.50\$187.50
  4. D
    $150\$150

Answer

The restorer must sell each of the remaining tablets for $250\$250.
The total investment includes the bulk purchase price (40×$120=$4,80040 \times \$120 = \$4,800) plus the cost of replacement parts ($1,200\$1,200), which totals $6,000\$6,000. A 25%25\% profit on a $6,000\$6,000 investment requires $1,500\$1,500 in profit, meaning the total revenue must reach $7,500\$7,500. Because 1010 tablets were discarded, the restorer only has 3030 tablets left to sell. Dividing the target total revenue by the 3030 remaining tablets ($7,500÷30\$7,500 \div 30) gives a required selling price of $250\$250 for each functional tablet.

Step-by-Step Solution

1
Calculate the total cost of purchasing the tablets.
40 tablets×$120=$4,80040 \text{ tablets} \times \$120 = \$4,800
To determine the initial part of the investment.
2
Add the overhead costs to find the total investment.
$4,800+$1,200 (parts)=$6,000\$4,800 + \$1,200 \text{ (parts)} = \$6,000
Profit must be calculated based on the entire total investment, not just the purchase price.
3
Calculate the target total revenue required to achieve a 25%25\% profit.
$6,000×1.25=$7,500\$6,000 \times 1.25 = \$7,500
A 25%25\% profit means the revenue must be 125%125\% of the total investment.
4
Determine the number of functional tablets available to sell.
40−10=30 tablets40 - 10 = 30 \text{ tablets}
The discarded tablets generate no revenue, so the entire target revenue must be generated by the remaining inventory.
5
Calculate the required selling price per functional tablet.
$7,500÷30=$250\$7,500 \div 30 = \$250
Dividing the target total revenue by the number of sellable items gives the unit selling price.

Key Concept

Profit and Loss with Overhead and Inventory Shrinkage
Estimated Time:1m 30s
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Topics

Profit and Loss

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