Percentages 37
is 63 mm. 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 is 2.38% too high,
which is sometimes written as + 2.38% error.
Problem 18. The voltage across a component in
an electrical circuit is calculated as 50 V using
Ohm’s law. When measured, the actual voltage is
50.4 V. 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 is 0.79% 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 £149.50 in a sale for a
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 =
14 950
65
= £230
Problem 20. A couple buys a flat and make an
18% profit by selling it 3 years later for £153 400.
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
=
153 400
100 + 18
× 100
=
153 400
118
× 100 =
1 5 340 000
118
= £130 000
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 =
63 000
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?
is 63 mm. 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 is 2.38% too high,
which is sometimes written as + 2.38% error.
Problem 18. The voltage across a component in
an electrical circuit is calculated as 50 V using
Ohm’s law. When measured, the actual voltage is
50.4 V. 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 is 0.79% 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 £149.50 in a sale for a
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 =
14 950
65
= £230
Problem 20. A couple buys a flat and make an
18% profit by selling it 3 years later for £153 400.
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
=
153 400
100 + 18
× 100
=
153 400
118
× 100 =
1 5 340 000
118
= £130 000
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 =
63 000
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?