Exercises: Ratio, VAT, interest and speed

1. a) Divide €240 in the ratio $3 : 5$.
2. b) Write the ratio $45 : 60$ in its simplest form.
3. c) Find the value of $x$ if $3 : 7 = x : 28$.

A jacket costs €80 before VAT. VAT is charged at $23\%$.

1. a) Calculate the amount of VAT.
2. b) Calculate the total price including VAT.

1. a) A train travels at $90 \text{ km/h}$ for 2.5 hours. Calculate the distance travelled.
2. b) A cyclist travels $42 \text{ km}$ in 3 hours. Calculate her average speed.
3. c) A bus travels $150 \text{ km}$ at $60 \text{ km/h}$. Calculate the time taken.

Niamh invests €5,000 at $3\%$ per annum compound interest.

1. a) Calculate the value of the investment after 3 years, correct to the nearest cent.
2. b) Calculate the total interest earned.
3. c) Calculate how much more she would have earned with simple interest at $3\%$ over the same period, or state how much less, and explain.

Cathal earns €18.50 per hour and works 38 hours in a week. The standard rate of tax is $20\%$ on the first €800 of weekly gross pay and $40\%$ on the remainder. He has weekly tax credits of €70 and pays USC and PRSI totalling €48.

1. a) Calculate his gross pay.
2. b) Calculate his total tax before credits.
3. c) Calculate his tax after credits and his net pay.

Siobhán travels from Dublin to a holiday in the United Kingdom. The exchange rate is €1 = £0.85.

1. a) Convert €400 to pounds.
2. b) She spends £212.50 and converts the rest of her pounds back to euro at the same rate. How much does she receive?
3. c) A coat costs £68 in London. Find its price in euro.

A television is advertised at €599 including VAT at $23\%$.

1. a) Calculate the price before VAT, correct to the nearest cent.
2. b) During a sale the price including VAT is reduced by $15\%$. Calculate the new price.
3. c) Explain why reducing the price before VAT by $15\%$ and then adding VAT gives the same final price.

A sum of money $P$ is invested at compound interest. After 2 years it is worth €5,512.50 and after 3 years it is worth €5,788.13 (to the nearest cent).

1. a) Find the annual rate of interest.
2. b) Find the original sum $P$.
3. c) Find the value after 10 years, correct to the nearest euro.

A car travels from Cork to Dublin, a distance of $260 \text{ km}$. It travels the first $120 \text{ km}$ at $80 \text{ km/h}$ and the rest at $100 \text{ km/h}$.

1. a) Calculate the total journey time in hours and minutes.
2. b) Calculate the average speed for the whole journey, correct to one decimal place.
3. c) Explain why the average speed is not $90 \text{ km/h}$.