Que: A trader buys a batch of 120,000 computer chips for $3,600,000. He sells ....

[Max@Math Revolution]

Que: A trader buys a batch of 120,000 computer chips for $3,600,000. He sells \(\frac{2}{5}\) of the computer chips, each at 25 percent above the cost per computer chip. Later, he sells the remaining computer chips at a price per computer chip equal to 25 percent less than the cost per computer chip. What was the percent profit or loss on the batch of computer chips?

(A) Loss of 1%
(B) Loss of 5%
(C) Loss of 7.50%
(D) Profit of 10%
(E) Profit of 22.22%

[Max@Math Revolution]

Solution: Total cost of the 120,000 computer chips = $3,600,000

=> Cost of \(\frac{2}{5}\) of the above computer chips = $ 3,600,000 * \(\frac{2}{5}\) = $1, 440, 000.

These were sold at a 25% higher than the cost price. Thus, the selling price of the above computer chips

=> \(\frac{125}{100}\) *$1,440,100 = $1, 800, 000

Cost of the remaining computer chips = $(3, 600, 000 − 1, 440, 000) = $2, 160, 000

Later, these remaining computer chips were sold at a 25% lower than the cost price. Thus, the selling price of the above computer chips

=> \(\frac{75}{100}\) * $2, 160, 000= $1, 620, 000

Thus, total selling price = $(1, 800, 000 + 1, 620, 000) = $3, 420, 000.

Since total selling price (= $3,420,000) < total cost price (= $3,600,000), there is a loss

Thus, percent loss = \(\frac{\left(Cost\ price\ -\ Selling\ price\right)}{Cost\ price}\) × 100 (%)

=> \(\frac{\left(3,600,000\ -\ 3,420,000\right)}{3,600,000}\) × 100 (%) = -5% (Loss)

Therefore, B is the correct answer.

Answer B

[Scott@TargetTestPrep]

Que: A trader buys a batch of 120,000 computer chips for $3,600,000. He sells \(\frac{2}{5}\) of the computer chips, each at 25 percent above the cost per computer chip. Later, he sells the remaining computer chips at a price per computer chip equal to 25 percent less than the cost per computer chip. What was the percent profit or loss on the batch of computer chips?

(A) Loss of 1%
(B) Loss of 5%
(C) Loss of 7.50%
(D) Profit of 10%
(E) Profit of 22.22%

Solution:

The purchase price of each chip and the number of chips sold are red herrings; they can be any number. If we let $10 be the purchase price of each chip and 10 be the number of chips bought, then the cost is 10 x 10 = $100. He sold 2/5 x 10 = 4 chips for $12.50 each, and 3/5 x 10 = 6 chips for $7.50 each. Thus, the revenue is 4 x 12.50 + 6 x 7.50 = 50 + 45 = $95. We see that the revenue is $5 less than the cost of $100. In other words, the trader incurs a 5% loss on the sale of the chips.

Solution: B