Question

The mean proportional of a and b is 10 and the value of a is four times the value of b. If a > 0, b > 0, find the value of a + b?

Answer 1

It is given that,
$$\begin{gathered} a:10::10:b \\ \Rightarrow \frac{a}{10}=\frac{10}{b} \\ \Rightarrow a\times b=10\times 10 \\ \Rightarrow a\times b=100....\left(1\right) \end{gathered}$$

and $a=4b....\left(2\right)$

From (1) and (2),
$$\begin{gathered} \left(4b\right)b=100 \\ \Rightarrow b\times b=\frac{100}{4} \\ \Rightarrow b\times b=25 \\ \Rightarrow b\times b=5\times 5 \\ \Rightarrow b=5 \\ \Rightarrow a=4\times 5\left[\mathrm{From}\left(1\right)\right] \\ \Rightarrow a=20 \end{gathered}$$

$$\begin{gathered} \therefore a+b=20+5 \\ =25 \end{gathered}$$

Hence, a + b = 25.