Question

Which number is greater and by how much: A decreased by 50% and then increased by 50% of the result

Answer 1

The original
`A` would be greater than the new value by
`0.25\, A`.

Explanation:

Refer to the diagram attached.

`50\%` of
`A` is equivalent to
`0.5\, A`.

Reducing
`A` by
`50\%` is the same as subtracting
`0.5\, A` from
`A\!`. The "result" would be
`A - 0.5\, A = 0.5\, A`.

Since the "result" is
`0.5\, A`,
`50\%` of the "result" would be
`50\% * 0.5\, A = 0.5* 0.5\, A = 0.25\, A`.

Adding
`50\%` of the "result" to the result itself would be the same as adding
`0.25\, A` to
`0.5\, A`, which gives the new value
`0.75\, A`.

Thus, the original
`A` would be greater than the new value by
`A - 0.75\, A = 0.25\, A`.