Of the three numbers, the first is twice the second and the second is

1.	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 ?
Answer» 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, \(\frac{7}{4x} = 3\times\frac{7}{72}\) ⇒ 4x = 24 ⇒ x = 6 ∴ The three numbers are 4 × 6, 2 × 6, 6, i.e., 24, 12, 6.

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 ?

Answer»

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, \(\frac{7}{4x} = 3\times\frac{7}{72}\) ⇒ 4x = 24 ⇒ x = 6

∴ The three numbers are 4 × 6, 2 × 6, 6, i.e., 24, 12, 6.

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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 \(\frac{7}{72}\) . What are the three numbers ?

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