Problem
During a period of economic hardship, a factory’s profit X drops by 60%. After the downturn, profits increase by 80%. What is the final profit Y?
– 0.70X
– 0.72X
– Greater than X
Introduction
This question, taken from an aptitude test, challenges your ability to apply percentage changes in a real-world scenario. A common mistake is to assume that a 60% decrease followed by an 80% increase cancel each other out. They don’t. Let’s walk through the steps to find the correct answer.
Step 1 – Apply the 60% Decrease
The initial profit is X.
A 60% decrease leaves 40% of the original amount:
100% − 60% = 40%
In decimal form:
X × 0.40 = 0.40X
So, the profit drops to 0.40X.
Step 2 – Apply the 80% Increase
The 80% increase now applies to the reduced profit, not the original.
An 80% increase means multiplying by 1.80:
0.40X × 1.80 = 0.72X
So, the final profit Y equals 0.72X.
Correct Answer
0.70X → Incorrect: the result is too low.
0.72X → Correct.
Greater than X → Incorrect: 0.72X is still less than X.
Common Mistakes
Linear thinking: Assuming “–60% + 80% = +20%” ignores that the second change is based on a reduced value.
Wrong reference point: Forgetting the 80% increase applies to 0.40X, not the original X.
Faulty intuition: Assuming a larger percentage gain means you’ll end up with more than what you started with, without checking the math.
Did You Know?
After a 60% drop, the value becomes 0.40X. To get back to X, you’d need:
X ÷ 0.40X = 2.5
So, a 150% increase would be required—not just 80%. This shows why understanding base values is crucial in percentage problems.
Conclusion
After a 60% decrease followed by an 80% increase, the final profit is 0.72X—less than the original amount. Mastering how to apply percentage changes to changing reference points is key to solving these types of questions accurately.
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