Question

Mark the correct alternative in the following question:

The mean proportional of a and b is 10 and the value of a is four times the value of b. The value of a + b (a > 0, b > 0) is

(a) 20 (b) 25 (c) 101 (d) 29

Answer 1

$$\begin{gathered} \mathrm{Since},\mathrm{the}\mathrm{mean}\mathrm{proportional}\mathrm{of}\mathrm{two}\mathrm{positive}\mathrm{numbers}a\mathrm{and}b\mathrm{is}\mathrm{the}\mathrm{positive}\mathrm{number}x\mathrm{such}\mathrm{that}\frac{a}{x}=\frac{x}{b}. \\ \Rightarrow \frac{a}{10}=\frac{10}{b} \\ \Rightarrow ab=100 \\ \mathrm{But}a=4b \\ \Rightarrow 4b\times b=100 \\ \Rightarrow b^2=\frac{100}{4} \\ \Rightarrow b^2=25 \\ \Rightarrow b=\sqrt{25} \\ \Rightarrow b=5 \\ \Rightarrow a=4\times 5=20 \\ \therefore a+b=20+5=25 \end{gathered}$$

Hence, the correct alternative is option (b).