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A number is decreased by 25% and then increased by 25%. What is the final value

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Question: A number is decreased by 25% and then increased by 25%. What is the final value in terms of the original number? (2023)

Options:

  1. Original number
  2. Less than original
  3. More than original
  4. None of the above

Correct Answer: Less than original

Exam Year: 2023

Solution: 

Let the original number be x. After a 25% decrease, it becomes 0.75x. After a 25% increase, it becomes 0.75x * 1.25 = 0.9375x, which is less than the original number.

A number is decreased by 25% and then increased by 25%. What is the final value

Practice Questions

Q1
A number is decreased by 25% and then increased by 25%. What is the final value in terms of the original number? (2023)
  1. Original number
  2. Less than original
  3. More than original
  4. None of the above

Questions & Step-by-Step Solutions

A number is decreased by 25% and then increased by 25%. What is the final value in terms of the original number? (2023)
  • Step 1: Let the original number be x.
  • Step 2: Calculate 25% of x. This is 0.25x.
  • Step 3: Decrease the original number by 25%. This means you subtract 0.25x from x: x - 0.25x = 0.75x.
  • Step 4: Now, take the new value (0.75x) and calculate 25% of it. This is 0.25 * 0.75x = 0.1875x.
  • Step 5: Increase the new value (0.75x) by 25%. This means you add 0.1875x to 0.75x: 0.75x + 0.1875x = 0.9375x.
  • Step 6: The final value after both operations is 0.9375x, which is less than the original number x.
  • Percentage Change – Understanding how to calculate percentage decreases and increases and their cumulative effect on a number.
  • Order of Operations – Applying operations in the correct sequence to arrive at the final value.
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