SSC CGL 2024 Tier-I · 12 September 2024, Shift 2 · Quantitative Aptitude · Question 17 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.

In triangle ABC, the length of side BC is 2 cm less than twice the length of side AB. The length of side AC exceeds the length of side AB by 10 cm. The perimeter of the triangle is 40 cm. Determine the length (in cm) of the smallest side of the triangle.

(a)12
(b)10
(c)14
(d)8

Answer

Why

Correct — D. Name the side that every other side is measured against: let AB = x.

BC = 2x − 2 ('2 cm less than twice AB')
AC = x + 10 ('exceeds AB by 10 cm')
Perimeter: x + (2x − 2) + (x + 10) = 40
4x + 8 = 40, so 4x = 32 and x = 8

The sides are AB = 8, BC = 14, AC = 18, so the smallest is 8 cm → option (d)

Why the others are wrong

(a)
12 — Put AB = 12 and the sides become 12, 22 and 22 — a perimeter of 56 cm, 16 cm past the 40 the question fixes.
(b)
10 — 10 is the amount by which AC exceeds AB, lifted straight out of the stem. Put AB = 10 and the perimeter comes to 48 cm, not 40.
(c)
14 — 14 cm is BC, the middle side (2 × 8 − 2). It is a genuine side of this triangle, just not the smallest one.

Concept

Every relation in the stem is written against AB, so AB is the side to call x. Naming BC or AC instead forces fractions for no gain.

Then translate each clause literally: 'two less than twice AB' is 2x − 2, and 'exceeds AB by 10' is x + 10. The perimeter gives one linear equation in one unknown.

Solving is the easy half. The question asks for the smallest side, so the three lengths have to be listed and compared before anything is ticked.

Check that the triangle can exist: 8 + 14 = 22 > 18, so the three lengths do close.

A perimeter can be satisfied by numbers that no triangle could have, and the check costs ten seconds.

Key facts

AB = 8 cm, BC = 14 cm and AC = 18 cm add to the stated perimeter of 40 cm.
'2 cm less than twice AB' translates to 2x − 2, not 2(x − 2).
Any two sides of a triangle must exceed the third, and 8 + 14 > 18 holds here.

Study next

Translating worded side relations into a single linear equationThe triangle inequality used as a validity check on computed sidesPerimeter problems that ask for the largest or the smallest side rather than a named one

Common traps

Solving for x correctly and then reporting BC or AC instead of the smallest side.
Reading 'two less than twice AB' as 2(AB − 2), which gives 2x − 4.
Choosing AC or BC as the variable, which turns the perimeter equation into fractions.

The same translate-then-solve step carries SSC's age items.

At 19 Sep 2024, 12:30, Quant Q.6 a brother's age is set as 'three years less than twice' another's and both present ages are wanted — identical grammar, different dressing.

Related PYQs

No directly related past PYQ was found.