A shopkeeper sells some toys at $96 each. What is his profit percentage? (1) The profit is as much percentage as its cost price. (2) If the article is sold at half the price, there will be a loss of 20%.
Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Using Statement (1), we can set up the equation CP^2 + 100CP - 9600 = 0, which uniquely determines the cost price as \$60, allowing us to find the profit percentage. Using Statement (2), selling at half price (\$48) results in a 20% loss, which directly gives the cost price as 48 / 0.8 = $60, also allowing us to find the profit percentage. Thus, each statement alone is sufficient.
Using statement (1), let the cost price be x, so the profit percentage is also x; applying the profit percentage formula gives 96 = x + (x^2/100). Solving the quadratic equation x^2 + 100x - 9600 = 0 results in x = 60, which determines the profit percentage. Using statement (2), selling at half price equals 48 and results in a 20% loss, meaning 48 is 80% of the cost price; calculating 48 divided by 0.80 yields a cost price of 60, which allows calculating the profit percentage for a 96 selling price. Since the profit percentage can be found using either statement independently, each statement alone is sufficient.