# Difficult Averages Solved QuestionAptitude Discussion

 Q. 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 (dfrac{7}{72}) .The numbers are:
 ✖ A. 16, 8, 4 ✖ B. 20, 10, 5 ✔ C. 24, 12, 6 ✖ D. 36, 18, 9

Solution:
Option(C) is correct

Let three numbers be $x, y,z$

Given $x=2y⇒x=4z;y=2z;z=z$

The average of reciprocal numbers is $\dfrac{7}{72}$

$\dfrac{1/x+1/y+1/z}{3}=\dfrac{7}{72}$

$\dfrac{xy+yz+zy}{3xyz}=\dfrac{7}{72}$

$\dfrac{2z^2+4z^2+8z^2}{3Ã—4zÃ—2zÃ—z}=\dfrac{7}{72}$

$\dfrac{7}{12z}=\dfrac{7}{72}$

$z=\dfrac{504}{84}$

$z=6$

$⇒x=4×6$ = 24

## (3) Comment(s)

Sri Devi
()

yes...verification through options is the quickest method. however, if anyone wants any other alternative, here is one: :)

f=2s => s=(f/2) ..... (i)

s=2t => t=(s/2) ..... (ii)

(i) & (ii) clearly show that f, f/2, f/4 are the required numbers :)

now,

((1/f)+(2/f)+(4/f))/3=(7/72) (given that avg of reciprocals is 7/72)

7/f = 7/24 => f=24

there is no need to determine the rest of the two numbers as there is only one option with 24 as one of the numbers :)

Vivek
()

let

3rd no=1

2nd no=2

1st no= 4

now according to question

=>(1/4x+1/2x/+1/x)/3= 7/72

=>(1+2+4)/4x= 7/24

=>4x=24

=>x=6

now it can be said that 3rd no is 6 2nd is 12 and 1st is 24.

Paramjot
()

This is the type of question which can also be simply & fast solve through options.