1. The problem states that the numbers 40 and P are in the ratio 4:3, and their prime factors are represented in a Venn diagram. 2. First, express 40 as its prime factors: $$40 = 2^3 \times 5$$. 3. The ratio is given as 4:3 for 40 and P respectively, so we can write: $$\frac{40}{P} = \frac{4}{3}$$ 4. Solve for P: $$P = \frac{3}{4} \times 40 = 30$$ 5. Now, factorize P = 30 into prime factors: $$30 = 2 \times 3 \times 5$$ 6. From the Venn diagram, the common prime factors between 40 and P are 2 and 3 (since 40 has 2 and 5, and P has 2, 3, and 5, but the diagram shows 2 and 3 in the intersection). 7. The question asks for the value of p and r. Assuming p and r represent the unique prime factors in the Venn diagram: - p is the unique prime factor of P outside the intersection, which is 5. - r is the unique prime factor of 40 outside the intersection, which is 5. 8. Therefore: $$p = 5$$ $$r = 5$$