Ratio, proportion and rates of change

Amir and Beth share £240 in the ratio 5 : 3. Amir then gives Beth £30. Work out the new ratio of Amir's money to Beth's money in its simplest form.

y is inversely proportional to x². When x = 2, y = 12. Find y when x = 4.

£4,500 is invested at 3.5% compound interest per year. Work out the value of the investment after 4 years. Give your answer to the nearest penny.

In a sale, prices are reduced by 15%. A coat costs £68.85 in the sale. Work out the price before the sale.

A train travels 126 km in 45 minutes. (a) Work out its average speed in km/h. (b) Convert this speed to metres per second.

The population of a town rose from 48,200 to 53,750. Work out the percentage increase to 1 decimal place.

In a sale, prices are reduced by 40%. A coat costs £51.00 in the sale. Work out the price before the sale.

A car is bought for £12,000. Its value depreciates by 8% each year. Work out its value after 3 years, to the nearest pound.

Metal A has density 8 g/cm³. A block of metal A has volume 25 cm³ and is melted together with 300 g of metal B to make an alloy of volume 55 cm³ (metal B has density 10 g/cm³). Work out the density of the alloy.

A cyclist accelerates uniformly from rest to 12 m/s in 8 s, travels at 12 m/s until t = 30 s, then decelerates uniformly to rest at t = 42 s. (a) Work out the acceleration. (b) Work out the total distance travelled.

y is inversely proportional to x². When x = 3, y = 45. Find y when x = 5.