A varies directly with B when C is constant and inversly with C when B is constant . A=6, when B=2 and C=3. What is the value of A, when B=3 and C=18?

Options

A. `(1)/(2)`
B. `(5)/(2)`
C. `(3)/(2)`
D. `(7)/(2)`

Answer

C

Explanation

`"Given", A alpha B " " (1) ("C is constant.")`
`A prop (1)/(C) " " (2) ("B is constant.")`
From Eqs (1) and (2), we get
`A = (KB)/(C)," where " K " is constant".`
`(AC)/(B) = K`
(i) A = 6, B = 2, and C = 3
`therefore K = (6 xx 3)/(2) = 9`
(ii) A = ?, B = 3, and C = 18
`(A xx 18)/(3) = 9`
`rArr A = (3)/(2)`
Hence, the correct option is (c).