A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the original number?

Let's denote the original number as x.

Step 1: The number is decreased by 10%. This means the number becomes 90% of the original number. So, it becomes 0.9x.

Step 2: This number is then increased by 10%. This means the number becomes 110% of the decreased number. So, it becomes 1.1 * 0.9x = 0.99x.

Step 3: According to the problem, this number is 10 less than the original number. So, we can set up the equation 0.99x = x - 10.

Step 4: Solve this equation for x. If you subtract 0.99x from both sides, you get 0.01x = 10.

Step 5: Finally, divide both sides by 0.01 to solve for x. x = 10 / 0.01 = 1000.

So, the original number was 1000.