Jack and Sadia work for a company that sells boxes of breakfast cereal - Edexcel - GCSE Maths - Question 12 - 2018 - Paper 1

To find out by what percentage Sadia needs to reduce the price, we first need to establish the new quantity of cereal in Jack's offer.

1. Suppose each box originally contained 100g of cereal.

2. Jack's idea adds 25% more, so:

   $ext{Cereal in Jack's box} = 100g + 0.25 imes 100g = 125g$

3. Let the original price of the box be $P.

4. Then, the price per gram of cereal under Jack's offer is:

   $ext{Price per gram}_{Jack} = \frac{P}{125}$

5. For Sadia’s idea, the price per gram of cereal remains the same, thus:

   $ext{Price per gram}_{Sadia} = \frac{P'}{100}$ where $P'$ is the new price Sadia will set.

6. We want these two price per gram values to be equal:

   $\frac{P'}{100} = \frac{P}{125}$

7. Cross-multiplying gives:

   $125P' = 100P$

8. Therefore:

   $P' = \frac{100P}{125} = 0.8P$

9. This means Sadia needs to set her new price to 80% of the original price.

10. Hence, the reduction in price is:

$\text{Reduction} = P - P' = P - 0.8P = 0.2P$

11. The percentage reduction is then calculated as follows:

$\text{Percentage Reduction} = \frac{0.2P}{P} \times 100\% = 20\%$

Thus, Sadia needs to reduce the price by 20%.