SSC CGL 2025 Tier-I · 13 September 2025, Shift 2 · Quantitative Aptitude · Question 4 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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Determine the ratio of the number of students who play Football to the number of students who play Basketball in a survey of 120 students from the following table: Category | Number Play Football and Basketball | 25 Play Football but not Basketball | 45 Play Basketball but not Football | 35 Play neither sport | 15

(a)6:7
(b)7:5
(c)7:6
(d)5:7

Answer

Why

Correct — C. Each sport's total must include the students who play both.

Football = both + football only = 25 + 45 = 70
Basketball = both + basketball only = 25 + 35 = 60
Football : Basketball = 70 : 60
Divide by 10: 7 : 6 → option (c)

Check: 25 + 45 + 35 + 15 = 120, the survey size.

Why the others are wrong

(a)
6:7 — This is Basketball : Football, the order reversed. The question names Football first, and 70 football players outnumber 60 basketball players, so the first term must be larger.
(b)
7:5 — Football's 70 is right, but 50 is not the basketball count. It is the number who do not play football (35 + 15). Basketball is 25 + 35 = 60.
(d)
5:7 — It puts football below basketball, which the table contradicts: 70 against 60. 5 : 7 matches the 'both' row against the 'basketball but not football' row, 25 : 35.

Concept

A two-sport survey splits students into four boxes that do not overlap: both, football only, basketball only and neither. The four add to the total, 120.

A sport's total is its 'only' box plus the both box, because a student who plays both is counted as a football player and as a basketball player. The 'neither' box belongs to neither total.

Key facts

n(F) = football only + both = 45 + 25 = 70.
n(B) = basketball only + both = 35 + 25 = 60.
n(F ∪ B) = n(F) + n(B) − n(both) = 70 + 60 − 25 = 105, and 105 + 15 who play neither = 120.

Study next

Two-set Venn diagrams: n(A ∪ B) = n(A) + n(B) − n(A ∩ B)Three-set Venn problems with 'exactly two' and 'at least one' regionsRatios whose order is fixed by the wording of the question

Common traps

Taking the 'but not' rows (45 and 35) as the sport totals and leaving out the 25 who play both.
Writing the ratio in the wrong order: the stem names Football first.

Here the Venn regions arrive as a table rather than a diagram, and the four rows must add to the survey total of 120. Reading a 'both, but not' region from a three-circle diagram is tested at 19 Sep 2024, 16:00, Reasoning Q.18.

Related PYQs

No directly related past PYQ was found.

Topic: Histogram, Frequency polygon, Bar diagram & Pie chart — all 104 SSC CGL questions on it, every solved shift.