Question

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

• 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.