Answer: APBQ : APBC=4:21 and AAQP : AABC= 3:28.
Explanation: given : Here ABC is a triangle where AP:PC=1:3
let AP=1x and PC=3x, where x is the common value of AP and PC.
And AQ:QB = 3:4, similarly, let AQ=3y and QB= 4y, where y is the common value of AQ and QB.
Thus, AC= AP+PC= 1x+3x=4x and AB= AQ+QB= 3y+4y=7y
since, we have to find out APBQ : APBC= AP×BQ: AB×PC= 1x×4y: 7y×3x=4xy:21xy=4:21
So, APBQ : APBC=4:21
Now, AAQP : AABC= AQ×AP:AB×AC= 3y×1x:7y×4x=3xy:28xy=3:28
Thus, AAQP : AABC= 3:28.
