When x is added to each of 9, 15, 21 and 31 the numbers so obtained are in proportion. What is the mean proportional between the numbers (3x - 2) and (5x + 4)?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& 45+5x=63+3x\\ & 2x+18\\ & x=9\\ & \text{Mean proportional}=\sqrt{\left(3x-2\right)\left(5x+4\right)}\\ & =\sqrt{\left(9\times 3-2\right)\left(5\times 9+4\right)}\\ & =\sqrt{25\times 49}\\ & =5\times 7\\ & =35\end{array}$$