Question

If AP:PQ = 1:2 and PQ:QB = 4:5, then Q divides line segment AB in the ratio of?

• A. 4:5
• B. 2:3
• C. 6:5
• D. 4:9

Answer 1

The correct option is C

6:5

Given AP:PQ = 1:2 and PQ:QB = 4:5.
$\frac{AP}{PQ}=\frac{1}{2}\Rightarrow \frac{AP}{PQ}+1=\frac{1}{2}+1\Rightarrow \frac{AP+PQ}{PQ}=\frac{3}{2}\Rightarrow \frac{AQ}{PQ}=\frac{3}{2}---------\left(1\right)\frac{QB}{PQ}=\frac{5}{4}-----------\left(2\right)$
Dividing equation (1) by (2)
$\Rightarrow \frac{AQ}{QB}=\frac{6}{5}$
Hence Q divides the line segment AB in the ratio of 6:5.