09. Percentage Change (Practice Questions)

Notes:

Calculator test

Q1-3 from Percentage of Amount & Percentage Change

Other questions must include:

at least one increase
at least one decrease
at least one with large numbers

A small tree is measured to be $2.6$ m in height

Two years later, it is measured to be $3.2$ m

Calculate the percentage change in the height of the tree over the two years to $1$ decimal place.

ANSWER: $23.1 \%$

Wrong Answers:

$22.5 \%$

$28.2 \%$

$16.7 %$

Workings:

The difference in height over the two years is $3.2-2.6-0.6$ m

So the percentage change is $\dfrac{0.6}{2.6}\times100=23.1 \%$

A car is bought for a price of $£15000$

$5$ years later, its value decreased to $£3500$

Calculate the percentage change in the value of the car after $5$ years to $1$ decimal place.

Answer: $76.7 \%$

Wrong answers:

$80.4 \%$

$72.3 \%$

$72.5 \%$

Workings:

The difference in value over the five years is $£15000-£3500=£11500$

So the percentage change is $\dfrac{11500}{15000}\times100=76.7 \%$

A house is bought in an expensive area for $£450000$

After several years, its value increases to $£724000$

Calculate the percentage change in the value of the house to $1$ decimal place.

Answer: $60.9\%$

Wrong Answers:

$70.2\%$

$55.5 \%$

$68.3 \%$

Working:

The difference in value over the time period is $£724000-£450000=£274000$

So the percentage change is $\dfrac{274000}{450000}\times100=60.9 \%$

A student is given a test score of $45\%$ on a Maths exam.

After doing some more revision, the student resits the test and achieves a score of $65\%$

Calculate the percentage change in the score after the second attempt to $1$ decimal place.

Answer: $44.4\%$

Wrong Answers:

$54.5\%$

$48.5 \%$

$25.4 \%$

Workings:

The difference in score over the two attempts is $65-45=20$

So the percentage change is $\dfrac{20}{45}\times100=44.4 \%$

A restaurant is expanding its outdoor seating area.

Calculate the percentage increase (to $1$ decimal place) if the number of outdoor seats increases from $34$ to $72$

Answer: $111.8 \%$

Wrong answers:

$120.4 \%$

$118.8 \%$

$126.5 \%$

Workings:

The difference in the number of seats is $72-34=38$

So the percentage change is $\dfrac{38}{34}\times100=111.8 \%$