If b is the mean proportion between a and c, then the mean proportion between (a² + b²) and (b² + c²) is:

1. a(b + c)

2. b(a + c)

3. c(a + b)

4. none of these

Assertion (A): If $\dfrac{a}{b} = \dfrac{c}{d}$, then $\dfrac{a+c}{b+d} = \dfrac{a}{b}$.

Reason (R): If two or more than two ratios are equal, then each ratio = $\dfrac{\text{sum of antecedents}}{\text{sum of consequents}}$.

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

Assertion (A): If 2x = 3y and 4y = 5z, then x : y : z is equal to 15 : 10 : 8.

Reason (R): If x = y and y = z, then we cannot find the ratio x : y : z.

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

The mean proportion between two numbers is 6 and their third proportion is 48. Find two numbers.