A number is increased by 15% and then decreased by 25% and the number becomes 22 less than the original number. The original number is:

Question: A number is increased by 15% and then decreased by 25% and the number becomes 22 less than the original number. The original number is :

Solution:
Let the number is = 100x

Now after 15% of increase = 100x + 15% of 100x = 115x
Now 25% decrease = 115x - 25% of 115x = 115x - 28.75x = 86.25x

Actual decreased = 100x - 86.25x = 13.75x

According to the question,
13.75x = 22
⇒ x = 22/13.75
⇒ 100x = (22/13.75) × 100
⇒ 100x = 160.

∴ Original number = 160.