Remember that percentage gain or loss is always expressed relative to the original amount. For example; percentage increase or decrease in the cost price (CP) of an item is expressed relative to the cost price.

Percentage error expresses the percentage by which an amount differs from the correct amount. For example, if an incorrect measurement is made, the percentage error is worked out in relation to the true (correct) value of the measurement.

Percentage gain= actual gain x 100

                               Cost price

Percentage loss= actual loss x 100

                               Cost price

Percentage error= actual error x 100

                                Cost price      

Example 1

A shopkeeper buys a television set for 160,000 FRS and sells it again for 200,000 FRS. What is the percentage profit (gain)?

Solution

Actual profit

= 200,000 frs – 160,000frs

= 40,000 FRS

Therefore; percentage profit= 40,000 FRS × 100 = 25 = 25%

                                                     160,000                100

Example 2

Suppose that the value of π was worked out using measuring cylinders and found to be 3.27, while the value of π correct to 4 significant figures (s.f.) is 3.142. Find the percentage error.

Solution

Actual error= 3.27 – 3.142= 0.128

:. Percentage error= 0.128 x 100= 4.1% (2 s.f.)

                                     3.142