percentage error calculation

[learningmath]

Can some one please explain how these two simple % error calculation have been solved and what is the logic behind it. I just can not get my head around this, more alternate solutions are welcomed.



Relay Zone 1 reach is set to 85% of its Zone 1 section impedance, with a -15% measurement error, therefore its value is

85% x (100-15)/100 = 72% ( I do not understand the mathematical logic behind this)

Another version with + error


Relay Zone 1 reach is set to 72% of its Zone 1 section impedance, with a +15% measurement error, therefore its value is


72% x 100 / (100 + 15) = 63% ( why 100 is on top at this time)

 

[Ishuda]

The following is the way I would tackle the problem but I don't get the same answer given for the second part:

The error is the Measurement minus the Set, so fractional Error (percentage error divided by 100) is given by

E = (M - S) / S

If we assume there is no bias in the Measurement and the Measurement is linear in S we have

M = a S.

Putting these together we have

E = a - 1
or
a = 1 + E

Given that E is -0.15 when S is 0.85 shows that a is equal to 0.85 in this case and
M = a S = 0.85 * 0.85 = 0.7225 or 72.25%

Using the same reasoning, for the second part we would have a equal to 1.15 and
M = 1.15 * 0.72 = 0.828.

If this is not correct, I too would appreciate an explanation of the problem.

 

[Quaid]

85% x (100-15)/100 = 72%

I do not understand the mathematical logic behind this

They are taking 85% of 85% and rounding the answer.

0.85 * 0.85 = 0.7225

72% x 100 / (100 + 15) = 63%

why 100 is on top at this time

If they intended to take 1.15% of 72%, they goofed!