# Exam-Style Question on Ratio and Percentage Change

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 717. This question is similar to one that appeared on a GCSE Higher paper in 2022. The use of a calculator is allowed.

(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.

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