The compound ratio of the inverse ratios of the ratios ` (bc)/a : a^(2) , (ca)/b : b^(2) " and " (ab)/c : c^(2) ` is -

Options

A. ` 1 : abc`
B. ` 1 : a^(2) b^(2) c^(2)`
C. ` a : a^(3) b^(3) c^(3)`
D. ` abc : 1 `

Answer

D

Explanation

The inverse ratio of the ratios
` (bc)/a : a^(2) , (ca)/b : b^(2) " and " (ab)/c : c^(2) " are " a^(2) : (bc)/a , b^(2) : (ca)/b " and " c^(2) : (ab)/ c` respectively .
` :. ` The compound ratio of these inverse ratios is
` a^(2) xx b^(2) xx c^(2) : (bc)/a xx (ca)/b xx (ab)/c = a^(2) b^(2) c^(2) : abc `
` = (a^(2)b^(2)c^(2))/(abc) = (abc)/1 = abc : 1 `
Hence the required compound ratio is abc : 1 .
` :. ` (d) is correct .