Percentages
Rates
Ratios
Pythagoras
Challenge Questions
100

A shirt costs $60, but is 25% off. How much is the shirt?

$45


100

A car travels 120km in 2 hours. How fast is the car going?

60km/hr

100

Simplify 12:20

3:5

100

A right angle triangle with the short sides 3cm and 5cm.

5.83

100

A jacket is on sale for $84 after a 30% discount.

What was the original price?

$120

200
Increase 123 by 17%

143.91


200

5 apples cost $4. How much does one apple cost?

80c

200

The ratio of boys to girls is 5 : 7.

There are 35 girls.

How many boys are there?

25

200

The hypotenuse is 13 cm.

One side is 5 cm.

Find the other side. (to the nearest cm)

12cm

200

Three friends share $180 in the ratio:

2 : 3 : 5

How much does each person receive?

2 parts = $36
3 parts = $54
5 parts = $90

300

A game originally cost $200. It's price was raised by 15%, then discounted by 20%. How much does it cost?

184

300

A cyclist rides 36 km in 1.5 hours.

Find the average speed.

24 km/h

300

A recipe needs flour and sugar in the ratio 3 : 2.

If you use 18 cups of flour, how much sugar is needed?

12

300

Find the short side of a right angle triangle with a hypotenuse of 16cm and a side of 10cm.

12.5cm (1dp)

300

The ratio of boys to girls is:

5 : 7

There are 28 girls.

How many students are there altogether?

48

400

My pocket money was $15/week when I was 13. Every year it increases by 25%. What is my pocket money amount when I turn 16 (to the nearest dollar).

$29/week

400

Shop A sells

8 cans for $7.20

Shop B sells

10 cans for $9.50

Which is the better buy?

Shop A

400

The ratio of red, blue and green marbles is

2 : 5 : 3

There are 40 marbles altogether.

How many blue marbles are there?

20

400

is a triangle with the sides 8cm, 6cm, and 10cm a right angle triangle?

Yes


400

Two runners complete a race.

Runner A:

  • 15 km in 1.5 hours

Runner B:

  • 24 km in 2 hours

Who is faster and by how much?

Runner A = 10 km/h
Runner B = 12 km/h

Runner B is faster by 2 km/h

500

I spent 8% of my money on a new cricket bat, which cost $120. How much money did I have before my purchase?

$1500


500

A tap fills 24 litres in 6 minutes.

At the same rate, how many litres will it fill in 20 minutes?

80 litres

500

8 ∶ 𝑥 = 56 ∶ 63

9

500

Do the numbers  5, 8, 10 form a Pythagorean triad?

Yes

500

A rectangular garden is 30 m long and 16 m wide.

A path goes diagonally across the garden.

The path is paved at $12 per metre.

There is a 25% discount on the total cost.

How much does the path cost?

$306