p and q are two numbers such that p > q - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 2

From the second statement, we can write the equation:

$\frac{p + 20}{q + 20} = \frac{5}{2}$

Cross-multiplying gives:

$2(p + 20) = 5(q + 20)$

This simplifies to:

$2p + 40 = 5q + 100$

Rearranging gives:

$2p - 5q = 60 \quad (2)$

Now we have two simultaneous equations:

1. $p - 5q = -20$
2. $2p - 5q = 60$

Subtracting equation (1) from equation (2):

$(2p - 5q) - (p - 5q) = 60 + 20$

This simplifies to:

$p = 80$

Substituting $p = 80$ back into equation (1):

$80 - 5q = -20$

This gives:

$5q = 100\Rightarrow q = 20$

Thus, the ratio of p to q is:

$p : q = 80 : 20$

This can be simplified to:

$\frac{80}{20} = 4$

Therefore, the final answer is:

4 : 1