SSC CGL 2024 Tier-I · 11 September 2024, Shift 2 · Quantitative Aptitude · Question 15 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

If 0.4x + 0.16y = 1.7 and 0.3x + 0.12y = 3.4, then which of the following is correct?

(a)The system has unique solution.
(b)The system has finitely many solutions but not unique.
(c)The system has infinitely many solutions.
(d)The system has no solution.

Answer

Why

Correct — D. Compare the three coefficient ratios.

a₁⁄a₂ = 0.4⁄0.3 = 4⁄3
b₁⁄b₂ = 0.16⁄0.12 = 4⁄3
c₁⁄c₂ = 1.7⁄3.4 = 1⁄2

The x and y ratios agree but the constant ratio does not, so the two lines are parallel and distinct.

Elimination check: multiplying the second equation by 4⁄3 gives 0.4x + 0.16y = 4.533…, which contradicts the first equation's 1.7. The system therefore has no solution — option (d).

Why the others are wrong

(a)
The system has unique solution. — A unique solution needs a₁⁄a₂ ≠ b₁⁄b₂. Both ratios here are 4⁄3, so the two lines share a slope and never meet at a single point.
(b)
The system has finitely many solutions but not unique. — Two straight lines meet at one point, at none, or at every point of a shared line. A finite count above one is geometrically impossible for a pair of linear equations.
(c)
The system has infinitely many solutions. — Infinitely many solutions need all three ratios equal, so c₁⁄c₂ would have to be 4⁄3. It is 1.7⁄3.4 = 1⁄2, which makes the lines parallel rather than coincident.

Concept

For a₁x + b₁y = c₁ and a₂x + b₂y = c₂ the whole classification sits in three ratios.

a₁⁄a₂ ≠ b₁⁄b₂ — the lines intersect, one solution.
a₁⁄a₂ = b₁⁄b₂ ≠ c₁⁄c₂ — parallel and distinct, no solution.
a₁⁄a₂ = b₁⁄b₂ = c₁⁄c₂ — the same line, infinitely many solutions.

The decimals are cosmetic. Multiplying both equations by 100 gives 40x + 16y = 170 and 30x + 12y = 340, and every ratio is unchanged.

The equations keep the constants on the right, so c₁ = 1.7 and c₂ = 3.4. Moving them left as a₁x + b₁y − c₁ = 0 flips both signs and leaves the ratio c₁⁄c₂ at 1⁄2.

Key facts

a₁⁄a₂ = b₁⁄b₂ ≠ c₁⁄c₂ means the lines are parallel and the system is inconsistent.
Here 0.4⁄0.3 = 0.16⁄0.12 = 4⁄3, while 1.7⁄3.4 = 1⁄2.
A pair of linear equations in two variables has zero, one or infinitely many solutions, never two.

Study next

Consistent versus inconsistent systems and the ratio testFinding the value of k for which a pair of equations has no solutionThe graphical meaning of intersecting, parallel and coincident lines

Common traps

Clearing the decimals in one equation only and then comparing ratios.
Treating equal coefficient ratios as proof of infinitely many solutions without checking the constants.
Reading 'finitely many but not unique' as a real possibility for two straight lines.

SSC states this as a one-line classification and slows the comparison down with decimals or fractions. No solving is required, only the three ratios.

Related PYQs

No directly related past PYQ was found.