Explanation:

- Start with the equation: 3P = 5Q = 15R.

- We want to express P, Q, and R in terms of a common variable.

- Set each to a common value, say K. Therefore, 3P = K, 5Q = K, and 15R = K.

- Solve each for P, Q, and R:

- P = K/3

- Q = K/5

- R = K/15

- Find P:Q:R by expressing each in terms of K:

- \( P : Q : R = \frac{K}{3} : \frac{K}{5} : \frac{K}{15} \)

- Remove K by finding a common factor (least common multiple of denominators 3, 5, 15 is 15):

- P = 5 (multiply by 5)

- Q = 3 (multiply by 3)

- R = 1 (multiply by 1)

- The correct ratio is 5:3:1.

Option 2 - 5 : 3 : 1