If `p : q = r : s = t : u = 2 : 3` , then `(mp+nr+ot)` : `(mq+ns+ou)` is

Options

A. `1:3`
B. `1:2`
C. `2:3`
D. `3:2`

Answer

C

Explanation

`{:("p : q","r : s","t : u"),(2:3,2:3,2:3):}`
`rArr (p)/(q)=(r)/(s)=(t)/(u)=(2)/(3)`
`rArr` Let `p=2x" "q=3x`
`r = 2x,s=3x`
`t=2x,u=3x`
`:. (mp+nr+ot)/(mg +ns+ou)`
`rArr(2xm+2xn+2xo)/(3xm+3xm+3xo)`
`=(m.2x+n.2x+0.2x)/(m.3x+n.3x+0.3x)`
`=(2x(m+n=o))/(3x(m+n+o))=(2)/(3)`.