8.2 Ratio and Rates

Simplify the ratio $18:24$ fully. State the HCF you used.

Simplify the ratio $12:18:30$ fully.

Write 9 hours out of 30 hours as a percentage.

In a bag there are 8 strawberry sweets and 12 orange sweets. Write the ratio of strawberry to orange in its simplest form.

Find 40% of 500 g.

Write $\dfrac{7}{20}$ as a percentage.

8 apples cost 2.40 chf. Find the cost of 1 apple.

Fill in the missing value so that $2:7$ is equivalent to $\square:28$.

Increase 80 chf by 15%.

Decrease 90 chf by 20%.

Simplify the ratio 210 mm : 14 cm : 35 cm.

Share 80 chf in the ratio $3:5$.

A bag of 25 sweets contains 15 raspberry sweets; the rest are pineapple. (a) Write the ratio raspberry : pineapple in simplest form. (b) What percentage of the sweets are pineapple?

8 chocolate bars cost 2.40 chf. How much would 20 chocolate bars cost at the same rate?

8 chocolate bars cost 2.40 chf. How many bars can be bought for 6.00 chf?

A car travels 360 km in 4 hours. Find its average speed in km/h and km/min.

A water tank fills at 8 L/min. How many litres in (a) 12 minutes? (b) 2 hours?

Find the unit rate: 24 chf for 8 kg of fruit.

An item that cost 200 chf is now 150 chf. Find the percentage decrease.

A salary of 5500 chf is increased by 6%. Find the new salary.

In a 3-leg relay, Stefania ran $\dfrac{2}{5}$ of the course, Jan ran 28% of the course, and René ran the rest. What percentage did René run?

A bike is on sale for 480 chf. This is a 20% discount on the original price. What was the original price? Give your answer to 2 decimal places.

If $x:y = 2:3$ and $x:z = 4:5$, find the ratio $y:z$ in its simplest form.

Out of 1200 competitors, 900 finished the race. The ratio of female : male finishers is $5:4$. Find the number of male finishers and the number of female finishers.

You earn 200 chf a week. Your boss gives you a 20% pay increase. The following week your new pay is cut by 10%. How much do you earn now?

Shop A: 10 bars for 2.50 chf. Shop B: 12 bars for 2.40 chf, plus 3 free bars. Which shop offers better value per bar?

A submarine is at $-120$ m. It rises by 20% of its current depth (towards the surface). What is its new depth?

Which of these ratios are equivalent to $2:5$? Pick all that apply.\nA: $6:15$, B: $10:20$, C: $8:20$.

A car travels 144 km in 2 hours. (a) Find the speed in km/h. (b) Convert to m/s.

A price of 80 chf is increased by 50% then decreased by 20%. What is the final price?

A long-sleeve shirt has 6 front buttons and 1 cuff buttons; a short-sleeve shirt has 4 front buttons and no cuff buttons. The factory uses 8 times as many front buttons as cuff buttons in total. Find the ratio of long-sleeve to short-sleeve shirts produced.

A price is increased by 50% and then decreased by 20%. Find the single percentage change equivalent to these two changes.

A jacket is reduced by 30% in a January sale, then by a further 10% in February. After both reductions it costs 63 chf. Find the original price.

In a class of 60 pupils, the ratio of pupils who walk to school to those who cycle is $4:1$. $\dfrac{1}{4}$ of the class take the bus and 5 pupils take the train. How many walk?

In a school the ratio of Year 7 : Year 8 : Year 9 is $7:6:5$. Year 7 has 140 pupils. (a) How many pupils are in Year 9? (b) What percentage of the school is in Year 8? Give your answer to 1 d.p.

A car depreciates by 15% in its first year and by 10% each subsequent year. If the car cost £30000 new, find its value after 3 years (to nearest £).

Currency: 1 chf = 0.98 EUR. A shopkeeper charges 2% commission on euro purchases. If a tourist exchanges 300 chf, how many euros do they receive?

A 10-litre solution is 60% acid. How much pure water must be added to dilute it to 40% acid?

Three friends share an inheritance in the ratio $2:3:5$. The eldest receives £1800 more than the youngest. Find each share.

Two prices fell by the same percentage. The first fell from £400 to £320; the second fell from £600 to $x$. Find $x$.