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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 $$\frac{7}{72}$$ . The numbers are:
Answer & Solution
Correct Answer:
Option
C
Let the number be x.
Then, second number = 2x.
First number = 4x.
∴ $$\frac{1}{x}$$ + $$\frac{1}{2x}$$ + $$\frac{1}{4x}$$ = $$\frac{7}{72}$$ × 3
⇒ $$\frac{7}{4x}$$ = $$\frac{7}{24}$$
⇒ 4x = 24
⇒ x = 6
So, the number are 24, 12 and 6
Then, second number = 2x.
First number = 4x.
∴ $$\frac{1}{x}$$ + $$\frac{1}{2x}$$ + $$\frac{1}{4x}$$ = $$\frac{7}{72}$$ × 3
⇒ $$\frac{7}{4x}$$ = $$\frac{7}{24}$$
⇒ 4x = 24
⇒ x = 6
So, the number are 24, 12 and 6
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