8.2 Ratio and Rates

Simplify the ratio $16:36$ fully. State the HCF you used.

Simplify the ratio $21:14:35$ fully.

Write 6 hours out of 24 hours as a percentage.

In a bag there are 5 strawberry sweets and 15 orange sweets. Write the ratio of strawberry to orange in its simplest form.

Find 60% of 600 g.

Write $\dfrac{3}{4}$ as a percentage.

12 apples cost 3.00 chf. Find the cost of 1 apple.

Fill in the missing value so that $3:5$ is equivalent to $\square:20$.

Increase 100 chf by 25%.

Decrease 125 chf by 25%.

Simplify the ratio 270 mm : 36 cm : 45 cm.

Share 60 chf in the ratio $2:3$.

A bag of 20 sweets contains 13 raspberry sweets; the rest are pineapple. (a) Write the ratio raspberry : pineapple in simplest form. (b) What percentage of the sweets are pineapple?

12 chocolate bars cost 3.00 chf. How much would 30 chocolate bars cost at the same rate?

12 chocolate bars cost 3.00 chf. How many bars can be bought for 4.50 chf?

A car travels 240 km in 3 hours. Find its average speed in km/h and km/min.

A water tank fills at 6 L/min. How many litres in (a) 12 minutes? (b) 2 hours?

Find the unit rate: 15 chf for 6 kg of fruit.

An item that cost 80 chf is now 60 chf. Find the percentage decrease.

A salary of 4000 chf is increased by 8%. Find the new salary.

In a 3-leg relay, Stefania ran $\dfrac{2}{5}$ of the course, Jan ran 35% of the course, and René ran the rest. What percentage did René run?

A bike is on sale for 590 chf. This is a 26% discount on the original price. What was the original price? Give your answer to 2 decimal places.

If $x:y = 4:5$ and $x:z = 3:7$, find the ratio $y:z$ in its simplest form.

Out of 2000 competitors, 1650 finished the race. The ratio of female : male finishers is $20:13$. Find the number of male finishers and the number of female finishers.

You earn 100 chf a week. Your boss gives you a 25% pay increase. The following week your new pay is cut by 25%. How much do you earn now?

Shop A: 12 bars for 3.00 chf. Shop B: 12 bars for 3.50 chf, plus 3 free bars. Which shop offers better value per bar?

A submarine is at $-80$ m. It rises by 25% of its current depth (towards the surface). What is its new depth?

Which of these ratios are equivalent to $3:4$? Pick all that apply.\nA: $9:12$, B: $15:18$, C: $21:28$.

A car travels 270 km in 3 hours. (a) Find the speed in km/h. (b) Convert to m/s.

A price of 100 chf is increased by 25% then decreased by 20%. What is the final price?

A long-sleeve shirt has 8 front buttons and 2 cuff buttons; a short-sleeve shirt has 6 front buttons and no cuff buttons. The factory uses 10 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 20% and then decreased by 25%. Find the single percentage change equivalent to these two changes.

A jacket is reduced by 20% in a January sale, then by a further 25% in February. After both reductions it costs 60 chf. Find the original price.

In a class of 40 pupils, the ratio of pupils who walk to school to those who cycle is $8:5$. $\dfrac{1}{4}$ of the class take the bus and 4 pupils take the train. How many walk?

In a school the ratio of Year 7 : Year 8 : Year 9 is $5:4:3$. Year 7 has 100 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 £20000 new, find its value after 3 years (to nearest £).

Currency: 1 chf = 1.04 EUR. A shopkeeper charges 2% commission on euro purchases. If a tourist exchanges 250 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 £1200 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 $x$.