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A company calculates its profit or loss quarterly. The company makes 25% profit, 20% loss and 20% loss in three consecutive quarters. What minimum profit or loss should the company make in fourth quarter to have no loss overall?
Explanation
To find the required profit or loss, assume the initial value of the company at the start of the first quarter is 100.
- Quarter 1: A 25% profit increases the value to 100 + (25% of 100) = 125.
- Quarter 2: A 20% loss decreases the value to 125 − (20% of 125) = 125 − 25 = 100.
- Quarter 3: A 20% loss decreases the value to 100 − (20% of 100) = 80.
To have "no loss overall," the value at the end of the fourth quarter must return to at least the initial value of 100. Let x be the required profit percentage in the fourth quarter:
80 + (x/100 × 80) = 100
0.8x = 20
x = 20 / 0.8 = 25
Thus, the company must make a minimum 25% profit in the fourth quarter to ensure the final value is not less than the starting value.
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