SSC CHSL 2024 PYQ — Question 59

The correct answer is option 1 i.e. 6

If a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0

Then, the following condition must be met for the pair of linear equations to have infinitely many solutions = a₁/a₂ = b₁/b₂ = c₁/c₂

Here, kx + 3y – ( k – 3 ) = 0 and 12x + ky – k = 0

a₁ = k; b₁ = 3; c₁ = -(k - 3) = 3 - k

a₂ = 12; b₂ = k; c₂ = -k

So, k/12 = 3/k = (3 - k)/(-k)

⇒ k/12 = 3/k

⇒ k² = 36

⇒ k = 6 (positive value required)

Now, 3/k = 3/6 = 1/2

Also, (3 - k)/(-k) = (3 - 6)/(-6) = (-3)/(-6) = 1/2

Thus, k = 6 satisfies both conditions.

Therefore, the required positive value of k is 6.