The price of 2 ratios are in x:y when the prices both increase by £20, the ratio becomes 5:2 when the prices both reduce by £5 the ratio becomes 5:1 express the x:y ratio in the lowest form

x:y = 4:1

Step-by-step explanation:

Since their ratios are x:y, when they both increase by £20, their ratio is 5:2.

So, x + 20/(y + 20) = 5/2   (1)

When they both decrease by £5, their ratio is 5:1.

So, x - 5/(y - 5) = 5/1    (2)

Simplifying (1) and (2), we have

x + 20/(y + 20) = 5/2  (1)

cross-multiplying, we have

2(x + 20) = 5(y + 20)

expanding the brackets, we have

2x + 40 = 5y + 100

2x - 5y = 100 - 40

2x - 5y = 60     (3)

So,

x -5/(y - 5) = 5/1  (2)

cross-multiplying, we have

(x - 5) = 5(y - 5)

expanding the brackets, we have

x - 5 = 5y - 25

x =  5y - 25 + 5

x = 5y - 20   (4)

Substituting (4 into (3), we have

2x - 5y = 60     (3)

2(5y - 20) - 5y = 60

10y - 40 - 5y = 60

10y - 5y = 60 + 40

5y = 100

y = 100/5 = 20

substituting y = 20 into (4), we have

x = 5y - 20   (4)

x = 5(20) - 20  

x = 100 - 20

x = 80

So, x/y = 80/20 = 4

x/y = 4/1

x:y = 4:1