36 Basic Engineering Mathematics
5.3.3 Percentage change
Percentage change is given by
new value − original value
original value
× 100%.
Problem 15. A box of resistors increases in price
from £45 to £52. Calculate the percentage change
in cost, correct to 3 significant figures
% change =
new value − original value
original value
× 100%
=
52 − 45
45
× 100% =
7
45
× 100
= 15.6% = percentage change in cost
Problem 16. A drilling speed should be set to
400 rev/min. The nearest speed available on the
machine is 412 rev/min. Calculate the percentage
overspeed
% overspeed =
available speed − correct speed
correct speed
×100%
=
412 − 400
400
×100% =
12
400
×100%
= 3%
Now try the following Practice Exercise
Practice Exercise 22 Further percentages
(answers on page 342)
1. Calculate 43.6% of 50 kg.
2. Determine 36% of 27 m.
3. Calculate, correct to 4 significant figures,
(a) 18% of 2758 tonnes
(b) 47% of 18.42 grams
(c) 147% of 14.1 seconds.
4. When 1600 bolts are manufactured, 36 are
unsatisfactory. Determine the percentage that
is unsatisfactory.
5. Express
(a) 140 kg as a percentage of 1 t.
(b) 47 s as a percentage of 5 min.
(c) 13.4 cm as a percentage of 2.5 m.
6. A block of Monel alloy consists of 70%
nickel and 30% copper. If it contains 88.2 g
of nickel, determine the mass of copper in the
block.
7. An athlete runs 5000 m in 15 minutes 20
seconds. With intense training, he is able to
reduce this time by 2.5%. Calculate his new
time.
8. A copper alloy comprises 89% copper, 1.5%
iron and the remainder aluminium. Find the
amount of aluminium, in grams, in a 0.8 kg
mass of the alloy.
9. A computer is advertised on the internet at
£520, exclusive of VAT. If VAT is payable at
17.5%, what is the total cost of the computer?
10. Express 325 mm as a percentage of 867 mm,
correct to 2 decimal places.
11. A child sleeps on average 9 hours 25 minutes
per day. Express this as a percentage of the
whole day, correct to 1 decimal place.
12. Express 408 g as a percentage of 2.40 kg.
13. When signing a new contract, a Premiership
footballer’s pay increases from £15 500 to
£21 500 per week. Calculate the percentage
pay increase, correct to 3 significant figures.
14. A metal rod 1.80 m long is heated and its
length expands by 48.6 mm. Calculate the
percentage increase in length.
15. 12.5% of a length of wood is 70 cm. What is
the full length?
16. A metal rod, 1.20 m long, is heated and
its length expands by 42 mm. Calculate the
percentage increase in length.
5.4 More percentage calculations
5.4.1 Percentage error
Percentage error =
error
correct value
× 100%
Problem 17. The length of a component is
measured incorrectly as 64.5 mm. The actual length
5.3.3 Percentage change
Percentage change is given by
new value − original value
original value
× 100%.
Problem 15. A box of resistors increases in price
from £45 to £52. Calculate the percentage change
in cost, correct to 3 significant figures
% change =
new value − original value
original value
× 100%
=
52 − 45
45
× 100% =
7
45
× 100
= 15.6% = percentage change in cost
Problem 16. A drilling speed should be set to
400 rev/min. The nearest speed available on the
machine is 412 rev/min. Calculate the percentage
overspeed
% overspeed =
available speed − correct speed
correct speed
×100%
=
412 − 400
400
×100% =
12
400
×100%
= 3%
Now try the following Practice Exercise
Practice Exercise 22 Further percentages
(answers on page 342)
1. Calculate 43.6% of 50 kg.
2. Determine 36% of 27 m.
3. Calculate, correct to 4 significant figures,
(a) 18% of 2758 tonnes
(b) 47% of 18.42 grams
(c) 147% of 14.1 seconds.
4. When 1600 bolts are manufactured, 36 are
unsatisfactory. Determine the percentage that
is unsatisfactory.
5. Express
(a) 140 kg as a percentage of 1 t.
(b) 47 s as a percentage of 5 min.
(c) 13.4 cm as a percentage of 2.5 m.
6. A block of Monel alloy consists of 70%
nickel and 30% copper. If it contains 88.2 g
of nickel, determine the mass of copper in the
block.
7. An athlete runs 5000 m in 15 minutes 20
seconds. With intense training, he is able to
reduce this time by 2.5%. Calculate his new
time.
8. A copper alloy comprises 89% copper, 1.5%
iron and the remainder aluminium. Find the
amount of aluminium, in grams, in a 0.8 kg
mass of the alloy.
9. A computer is advertised on the internet at
£520, exclusive of VAT. If VAT is payable at
17.5%, what is the total cost of the computer?
10. Express 325 mm as a percentage of 867 mm,
correct to 2 decimal places.
11. A child sleeps on average 9 hours 25 minutes
per day. Express this as a percentage of the
whole day, correct to 1 decimal place.
12. Express 408 g as a percentage of 2.40 kg.
13. When signing a new contract, a Premiership
footballer’s pay increases from £15 500 to
£21 500 per week. Calculate the percentage
pay increase, correct to 3 significant figures.
14. A metal rod 1.80 m long is heated and its
length expands by 48.6 mm. Calculate the
percentage increase in length.
15. 12.5% of a length of wood is 70 cm. What is
the full length?
16. A metal rod, 1.20 m long, is heated and
its length expands by 42 mm. Calculate the
percentage increase in length.
5.4 More percentage calculations
5.4.1 Percentage error
Percentage error =
error
correct value
× 100%
Problem 17. The length of a component is
measured incorrectly as 64.5 mm. The actual length