Question

Of the three numbers, the first is twice the second, and the second is twice the third. The average of the reciprocal of the numbers is $\frac{7}{72}$. What are the three numbers ?

• A. $24,12,6$
• B. $8,4,2$
• C. $12,6,3$
• D. None of the above

Answer 1

Answer: (A)

$24,12,6$

Let the third number be $x$

Then Second number $=2x$ and first number $=4x$
Sum of the reciprocals of these $3$ numbers $=$ $\frac{1}{4x}+\frac{1}{2x}+\frac{1}{x}=\frac{1+2+4}{4x}=\frac{7}{4x}$
Given, $\frac{7}{4x}=3\times \frac{7}{72}$

$\Rightarrow 4x=24$

$\Rightarrow x=6$

Therefore, the three numbers are $4\times 6,2\times 6,6$ i.e. $24,12,6$.