SSC CGL 2024 Tier-I · 17 September 2024, Shift 3 · Quantitative Aptitude · Question 17 of 98

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.

There are y yellow marbles and b blue marbles in a box. 18% of the yellow marbles were added to 24% of the blue marbles, and the total was 30. Three times the number of yellow marbles exceeds two times the number of blue marbles by 200. What is the ratio of y 2 to b 2 ?

(a)4 : 1
(b)6
(c)2
(d)5

Answer

Why

Correct — A. Turn the two sentences into two equations.

"18% of yellow added to 24% of blue was 30":
0.18y + 0.24b = 30 → ×100, then ÷6 → 3y + 4b = 500

"Three times yellow exceeds two times blue by 200":
3y − 2b = 200

Subtract the second from the first: 6b = 300 → b = 50
Put b = 50 back: 3y = 200 + 100 = 300 → y = 100

y² : b² = 100² : 50² = 10,000 : 2,500 = 4 : 1 → option (a).

Why the others are wrong

(b)
6 — 6 would need y² ⁄ b² = 6, so y ⁄ b = √6. The two equations force whole numbers, y = 100 and b = 50, and 100² ⁄ 50² is 4.
(c)
2 — 2 is y : b, not y² : b². Squaring a ratio squares both terms, so 2 : 1 becomes 4 : 1 — this is the answer of someone who stopped one line early.
(d)
5 — 5 would require y ⁄ b = √5. Solving the pair gives exactly y = 100 and b = 50, so the ratio of the squares is 4 : 1 and no surd enters this problem.

Concept

Two statements, two unknowns. One is a percentage sentence and the other a difference sentence, and each becomes a linear equation once the English is read literally.

'A exceeds B by 200' is A − B = 200. Clearing the decimals first, 0.18y + 0.24b = 30 becomes 3y + 4b = 500, which shares the coefficient 3y with the second equation — so simple subtraction eliminates y in one step. The final line is a ratio of squares, not of the numbers themselves.

The response sheet flattens the superscripts, so the stem prints as 'the ratio of y 2 to b 2'. Read those as y² and b² before solving; taken literally as multiplication the question would have no sensible answer.

Key facts

0.18y + 0.24b = 30 clears to 3y + 4b = 500 after multiplying by 100 and dividing by 6.
'Three times y exceeds two times b by 200' is 3y − 2b = 200.
Solving the pair gives y = 100 and b = 50.
y : b = 2 : 1, so y² : b² = 4 : 1 — squaring a ratio squares each term.

Study next

Word problems where one equation is hidden inside a percentage statementRatio of squares against ratio of terms, and when each is askedElimination by subtraction when one variable already carries matching coefficients

Common traps

Stopping at y : b = 2 : 1. The question asks for the ratio of the squares.
Reading 'exceeds two times blue by 200' backwards as 2b − 3y = 200, which yields a negative count.
Working with 0.18 and 0.24 as they stand and losing a decimal place. Multiplying through by 100 first keeps the arithmetic in whole numbers.

The story is marbles but the machinery is two linear equations, one of them dressed as a percentage.

Note the checkable finish: 18% of 100 is 18 and 24% of 50 is 12, and 18 + 12 = 30. Substituting back costs ten seconds and catches a sign error before it costs a mark.

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