SSC CGL 2024 Tier-I · 25 September 2024, Shift 3 · Quantitative Aptitude · Question 23 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 10 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.

Cindy bought 15 apples and 12 oranges and paid a sum of ₹447 for the purchase. Which of the statements given below is inconsistent with the information given in the previous statement, leading to no possible prices of the two fruits?

(a)Purchased 10 apples and 13 oranges and paid a sum of ₹353
(b)Purchased 25 apples and 20 oranges and paid a sum of ₹745
(c)Purchased 35 apples and 28 oranges and paid a sum of ₹1,029
(d)Purchased 12 apples and 8 oranges and paid a sum of ₹340

Answer

Why

Correct — C. Reduce the purchase to one equation and test each statement against it.

Let an apple cost ₹x and an orange ₹y.
15x + 12y = 447, and dividing by 3 gives 5x + 4y = 149.

Option (c) says 35x + 28y = 1029. Dividing by 7 gives 5x + 4y = 147.

The same left-hand side cannot be 149 and 147 at once, so option (c) admits no prices at all — it is the inconsistent statement.

Why the others are wrong

(a)
Purchased 10 apples and 13 oranges and paid a sum of ₹353 — Consistent. Solved with 5x + 4y = 149, the statement 10x + 13y = 353 gives x = 21, y = 11 — real, positive prices, so nothing is contradicted.
(b)
Purchased 25 apples and 20 oranges and paid a sum of ₹745 — Consistent. 25x + 20y = 745 divides by 5 to 5x + 4y = 149, the stem restated. It adds no information, but it rules nothing out either.
(d)
Purchased 12 apples and 8 oranges and paid a sum of ₹340 — Consistent. 12x + 8y = 340 divides by 4 to 3x + 2y = 85, which x = 21, y = 11 satisfies, since 63 + 22 = 85.

Concept

Two linear equations in two unknowns are inconsistent when their left sides are proportional and their constants are not — parallel lines that never meet.

Here 15x + 12y and 35x + 28y are both multiples of 5x + 4y, at 3 times and 7 times. The totals must therefore stand in the same 3:7 ratio.

447 × 7 ÷ 3 = 1043. So 35 apples and 28 oranges cost ₹1,043, and ₹1,029 is impossible whatever the two prices are.

The other three statements are all satisfied by x = 21 and y = 11, so the question is not which prices look right. It is which statement cannot be true at all.

Key facts

15x + 12y = 447 reduces to 5x + 4y = 149 on dividing by 3.
Prices of ₹21 an apple and ₹11 an orange satisfy the stem and options (a), (b) and (d).
35 apples and 28 oranges must cost 447 × 7 ÷ 3 = ₹1,043, so ₹1,029 cannot occur.
A pair of equations with proportional left sides and a non-proportional constant has no solution.

Study next

The conditions under which two linear equations have no solution, one solution, or infinitely manyElimination on two-variable price problemsRatio checks on scaled purchases, before any solving is attempted

Common traps

Solving all four options in full instead of scaling the stem equation once.
Calling option (b) wrong because it yields no unique prices — it is consistent, merely redundant.
Assuming the prices must be whole rupees. The test is consistency, not integrality.

SSC dresses a solvability condition as a shopping story, so the work is algebraic rather than arithmetic: reduce the stem to lowest terms and test each option against it. The scaling is the shortcut, since 15:12 and 35:28 both reduce to 5:4.

Related PYQs

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