Q43 / 90 · JEE Main 2012 (Offline) · Mathematics

If the line $2 x+y=k$ passes through the point which divides the line segment joining the points $(1,1)$ and $(2,4)$ in the ratio $3: 2$, then $k$ equals

A
$\frac{29}{5}$
B
$5$
Correct answer
C
$6$
D
$\frac{11}{5}$

Solution

Point $p=\left(\frac{6+2}{5}, \frac{12+2}{5}\right)$ $\mathrm{p}=\left(\frac{8}{5}, \frac{14}{5}\right)$ $p\left(\frac{8}{5}, \frac{14}{5}\right)$ lies on $2 x+y=k \quad \Rightarrow \frac{16}{5}+\frac{14}{5}=k \quad \Rightarrow k=\frac{30}{5}=6$

Hence, the correct answer is option: 'C'.

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