Question

If $a,b,c$are in GP and $4a,5b,4c$are in AP such that $a+b+c=70$, then value of $b$ is

• A. $5$
• B. $10$
• C. $15$
• D. $20$

Answer 1

The correct option is D

$20$

Explanation for the correct option:

Finding the value of $b$;

Given $a,b,c$ are in GP and

$a+b+c=70...\left(i\right)$

$4a,5b,4c$ are in AP

$$\begin{gathered} 2\left(5b\right)=4a+4c \\ 5b=2(a+c)....\left(ii\right) \end{gathered}$$

From $\left(i\right)$

$a+c=70-b$

Substitute this value in equation $\left(ii\right)$, we get

$$\begin{gathered} \Rightarrow 5b=2(70-b) \\ \Rightarrow 7b=140 \\ \Rightarrow b=20 \end{gathered}$$

$\therefore$Value of $b$ is $\mathbf{20}$.

Hence, Option (D) is correct