Exam-Style Questions.

(a) In an election, David Linewhip gained 27 552 votes out of a total of 43 715 votes. Write 27 552 as a percentage of 43 715 giving your answer to the nearest integer.

(b) Goodtrip Travel increases the cost of a holiday by 8%. The holiday originally cost £1245. Find the new cost of the holiday.

Worked Solution

In 2009 the price of a Big Mac was £2.29.

In 2013 the price of a Big Mac had risen to £2.69.

(a) Work out the percentage increase in the price of this snack over the four years.

(b) Express the price in 2009 as a percentage of the 2013 price.

(c) By what percentage must the 2013 price be discounted to equal the 2009 price?

Worked Solution

Davy Browning buys a premium skateboard.

He gets a discount of 15% off the normal price.

Davy pays £170 for the skateboard.

(a) Work out the normal price of the skateboard.

Saj invests £8000 in a savings account.

The savings account pays compound interest at a rate of 1.8% for the first year then 1.2% for each extra year.

(b) Work out the value of Saj’s investment at the end of 4 years.

Worked Solution

(a) Davy Browning earns £54000 per year before paying tax.
He pays tax on his earnings at a rate of 18%.
Calculate the amount Davy has after paying tax.

(b) Patty O’Dawes earns £57810 per year after paying tax at a rate of 18%.
Calculate the amount that Patty earns before paying tax.

(c) Davy opens a savings account with £2500.
The account pays 2.4% per year simple interest.
Calculate the amount in Davy’s account at the end of 5 years.

(d) Patty opens a savings account with £500 at the same time ad Davy.
The account pays 2.1% per year compound interest.
Patty pays another £500 into her account on the same day every year.
Find who has the greater amount in their account at the end of 5 years.

Worked Solution

The value of a new car is £22 000.

The value of the car decreases by 30% in the first year then 10% in each of the next 5 years.

Work out the value of the car after 6 years.

Worked Solution

Windthrup bought a car for £9500 which depreciated by 6% in the first year and 3.5% in the second year.

a) Windthrup thinks that in two years his car depreciated by 9.5% over the two years. Show, with any necessary calculations, that Winthrup is wrong.

b) Windthrup's car depreciates by \(x%\) during the third year. At the end of the three years the car is worth £8190. Find the value of \(x\) to three significant figures.

Worked Solution

Zoe invests £5000 in an account for one year. At the end of the year, interest is added to her account.

Zoe pays tax on this interest at a rate of 25%. After the tax has been taken off she received £25.40 interest.

Work out the percentage interest rate for the account.

Worked Solution

Montague invests £7000 for six years in a bank offering compound interest at \(x%\) per annum.

The investment is worth £7654.10 at the end of the six years.

Find the value of \(x\).

Worked Solution

John times how long it takes him to run around Hazelnut Park each Friday afternoon. The last three weeks his times, rounded to the nearest minute are \(p, q \; \text{and} \; r\).

He notices that \(q\) is 5% more than \(p\) and \(r\) is 5% less than \(q\).

Indicate which of the following statements are true:

(a) \( r \lt p \) and \( r \lt q \)

(b) \( r \gt p \) and \( r \gt q \)

(c) \( r = p \) and \( r \lt q \)

(d) \( p \gt q \) and \( p = r \)

(e) \( p =q \) and \( p \gt r \)

Worked Solution