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

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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:

  1. A. 36, 18, 9
  2. B. 24, 12, 6
  3. C. 20, 10, 5
  4. D. 16, 8, 4

Answer: Option B

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Solution(By ExamCraze Team)

$$eqalign{ & {text{Let}},{text{three}},{text{numbers}},{text{be}},x,,y,,z. cr & {text{Given}}, cr & x = 2y cr & Rightarrow x = 4z cr & Rightarrow y = 2z cr & Rightarrow z = z cr & {text{The}},{text{average}},{text{of}},{text{reciprocal}},{text{numbers}},{text{is}},frac{7}{{72}} cr & frac{{ { {frac{1}{x}} + {frac{1}{y}} + {frac{1}{z}} } }}{3} = frac{7}{{72}} cr & Rightarrow frac{{ {yz + xz + xy} }}{{3xyz}} = frac{7}{{72}} cr & Rightarrow frac{{2z times z + 4z times z + 4z times 2z}}{{3left( {4z times 2z times z} right)}} = frac{7}{{72}} cr & Rightarrow frac{{2{z^2} + 4{z^2} + 8{z^2}}}{{3 times 8{z^3}}} = frac{7}{{72}} cr & Rightarrow frac{{14{z^2}}}{{24{z^3}}} = frac{7}{{72}} cr & Rightarrow 504 = 84z cr & z = 6 cr & {text{So}},,x = 4z = 4 times 6 = 24, cr & Rightarrow y = 2z = 2 times 6 = 12 cr & {text{Thus}},{text{the}},{text{numbers}},{text{are}},24,,12,,6 cr} $$

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