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

Are you looking for correct answer of Of the three numbers the first is twice the second and…? Here we have shared detailed answer with explanations.

### 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

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}