Q207 / 270 · NDA 2019 (Phase 1) · Mathematics

If the lines $3 y+4 x=1, y=x+5$ and $5 y+b x=3$ are concurrent, then what is the value of $b$ ?

  • A
    1
  • B
    3
  • Correct answer
    C
    6
  • D
    1/2

Solution

Given lines, $3 y+4 x=1 \Rightarrow 4 x+3 y-1=0$ $\begin{aligned} & y=x+5 \Rightarrow x-y+5=0 \\ & 5 y+b x=3 \Rightarrow b x+5 y-3=0\end{aligned}$ Since, these lines are concurrent, $\begin{aligned} & \left|\begin{array}{ccc}4 & 3 & -1 \\ 1 & -1 & 5 \\ b & 5 & -3\end{array}\right|=0 \\ & \Rightarrow 4(3-25)-3(-3-5 \mathrm{~b})-1(5+\mathrm{b})=0 \\ & \Rightarrow 4(-22)+9+15 \mathrm{~b}-5-\mathrm{b}=0 \\ & \Rightarrow-88+4+14 \mathrm{~b}=0 \\ & \Rightarrow-84+14 \mathrm{~b}=0 \\ & \Rightarrow \mathrm{~b}=6\end{aligned}$

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

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