Basic Engineering Mathematics, Fifth Edition

Percentages 37

is 63mm. What is the percentage error in the

measurement?

% error=

error

correct value

×100%

=

64. 5 − 63

63

×100%

=

1. 5

63

×100%=

150

63

%

=2.38%

The percentage measurement error is2.38% too high,
which is sometimes written as+2.38% error.

Problem 18. The voltage across a component in

an electrical circuit is calculated as 50V using

Ohm’s law. When measured, the actual voltage is

50.4V. Calculate, correct to 2 decimal places, the

percentage error in the calculation

% error=

error

correct value

×100%

=

50. 4 − 50

50. 4

×100%

=

0. 4

50. 4

×100%=

40

50. 4

%

=0.79%

The percentage error in the calculation is0.79% too
low, which is sometimes written as−0.79% error.

5.4.2 Original value

Original value=

new value

100 ±% change

×100%

Problem 19. A man pays £149.50inasalefora

DVD player which is labelled ‘35% off’. What was

the original price of the DVD player?

In this case, it is a 35% reduction in price, so we

use

new value

100 −% change

×100, i.e. a minus sign in the

denominator.

Original price=

new value

100 −% change

× 100

=

149. 5

100 − 35

× 100

=

149. 5

65

× 100 =

14950

65

=£230

Problem 20. A couple buys a flat and make an

18% profit by selling it 3 years later for £153400.

Calculate the original cost of the house

In this case, it is an 18% increase in price, so we

use

new value

100 +% change

×100, i.e. a plus sign in the

denominator.

Original cost=

new value

100 +% change

× 100

=

153400

100 + 18

× 100

=

153400

118

× 100 =

15340000

118

=£130000

Problem 21. An electrical store makes 40% profit

on each widescreen television it sells. If the selling

price of a 32 inch HD television is £630, what was

the cost to the dealer?

In this case, it is a 40% mark-up in price, so we

use

new value

100 +% change

×100, i.e. a plus sign in the

denominator.

Dealer cost=

new value

100 +% change

× 100

=

630

100 + 40

× 100

=

630

140

× 100 =

63000

140

=£450

The dealer buys from the manufacturer for £450 and

sells to his customers for £630.

5.4.3 Percentage increase/decrease and

interest

New value=

100 +% increase

100

×original value

Problem 22. £3600 is placed in an ISA account

which pays 6.25% interest per annum. How much is

the investment worth after 1 year?