Question

If CR : RS = 2 : 3 and RS : SD = 5 : 6, then S divides line segment CD in the ratio .

• A. 5 : 8
• B. 18 : 24
• C. 25 : 18
• D. 5 : 12

Answer 1

The correct option is C 25 : 18

Given CR:RS = 2:3 and RS:SD = 5:6
$\frac{CR}{RS}=\frac{2}{3}\Rightarrow \frac{CR}{RS}+1=\frac{2}{3}+1\Rightarrow \frac{CR+RS}{RS}=\frac{5}{3}\Rightarrow \frac{CS}{RS}=\frac{5}{3}---\left(1\right)\frac{SD}{RS}=\frac{6}{5}---\left(2\right)$
Dividing equation (1) by (2),
$\Rightarrow \frac{CS}{SD}=\frac{25}{18}$
Hence S divides the line segment CD in the ratio of 25:18.