Question

Let $a,b,c$ are the Arithmetic means between two numbers such that $a+b+c=15$ and $p,q,r$ be Harmonic mean between same numbers such that $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=\frac{5}{3}$ then the numbers are

• A. $3,10$
• B. $3,12$
• C. $3,15$
• D. $9,1$

Answer 1

Answer: (D)

$9,1$

Let numbers be $x,y$

$3\left(\frac{x+y}{2}\right)=a+b+c=15$

$x+y=10$

$\frac{3}{2}(\frac{1}{x}+\frac{1}{y})=(\frac{1}{p}+\frac{1}{q}+\frac{1}{r})=\frac{5}{3}$

$\frac{1}{x}+\frac{1}{y}=\frac{10}{9}$

$x=9,y=1$

Hence, option 'D' is correct.