Exam-Style Questions.

(a) Audrey, Seymore and Mr Mushnic share potted plants in the ratio Audrey : Seymore : Mr Mushnic = 3 : 4 : 7. Seymore receives 12 plants. Calculate the total number of plants shared.

(b) In a sale, a plant shop reduces all prices by 15%.

(i) Crystal buys a cactus which has an original price of £8.60. Calculate how much Crystal pays for the cactus.

(ii) Ronette pays £39 for a hanging basket. Calculate the original price of the hanging basket.

(c) Orin invests some money. The rate of interest for the first year is 3.5%. At the end of the second year the overall percentage increase of Orin’s investment is 6.6%. Find the rate of interest for the second year to the nearest whole number.

(d) A radioactive substance decays at an exponential rate of 4% per day. The initial mass is 360g.

(i) Find the mass at the end of 9 days.

(ii) Find how many more whole days, after day 9, it takes for the mass to reduce to less than 200g.

Worked Solution

Rishi breeds fish in tanks. Some of the tanks are small and some are large.

There are 8 fish in each small tank and 28 fish in each large tank.

Rishi currently has 560 fish and the ratio of the number of fish in small tanks to the number of fish in large tanks is 4:1

Rishi says that less than 10% of the tanks are large tanks.

Is Rishi correct?

You must show all your working.

Worked Solution

Promise is going to make some chocolate pyramids to sell.

The ingredients are chocolate, honey butter and cornflakes. The ingredients are mixed in the ratio \(5:2:3\) respectively.

(a) How much of each ingredient will she need to make 800g of the mixture?

• A bar of chocolate weighs 200g and costs £2.80.
• A jar of honey butter contains 320g and costs £1.90.
• A packet of cornflakes contains 300 g and costs £2.40.

Promise makes 3.2 kg of the mixture, from which she can make 80 chocolate pyramids.

She charges 70p for each pyramid and sells all 80 of them.

(b) How much profit does she make?

Worked Solution

£580 is shared between Alice, Bally, Chris and Dean.

The ratio of the amount Alice gets to the amount Bally gets is 4 : 5

Chris and Dean each get 2.5 times the amount Alice gets.

Work out the amount of money that Bally gets.

Worked Solution

A shop sells mini packs of fruit gums of different sizes

• Orange fruit gums are sold in packs of 3.
• Strawberry fruit gums are sold in packs of 4.
• Banana fruit gums are sold in packs of 8.

On one busy day the ratio of packs of orange, strawberry and banana fruit gums sold was 4:5:6.

If total of 400 fruit gums were sold work out the number of packs of banana fruit gums sold

Worked Solution

There are some round counters and some square counters in a pot. The counters are either blue or green.

• The ratio of the number of round counters to square counters is 5:6
• The ratio of the number of blue counters to green counters is 2:7

(a) What is the least possible number of counters in the pot?

(b) If all the round counters are green work out the least possible number of square green counters that are in the pot.

Worked Solution