SSC CGL 2024 Tier-I · 26 September 2024, Shift 1 · Quantitative Aptitude · Question 13 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.

A number whose fifth part increased by 5 is equal to its third part decreased by 7. Find half of the number.

(a)150
(b)45
(c)80
(d)60

Answer

Why

Correct — B. Let the number be N and translate each phrase.

"Fifth part increased by 5" = N⁄5 + 5
"Third part decreased by 7" = N⁄3 − 7
Equate them: N⁄5 + 5 = N⁄3 − 7
Multiply through by 15: 3N + 75 = 5N − 105

Collect: 180 = 2N, so N = 90
The stem asks for half: 90 ⁄ 2 = 45 → option (b)

Why the others are wrong

(a)
150 — 150 as the half makes the number 300, and 300 fails the condition: 300⁄5 + 5 = 65 while 300⁄3 − 7 = 93.
(c)
80 — 80 as the half makes the number 160, and 160⁄5 + 5 = 37 against 160⁄3 − 7 ≈ 46.3. The two sides are not equal.
(d)
60 — 60 as the half makes the number 120, and 120⁄5 + 5 = 29 against 120⁄3 − 7 = 33. Close, but the equation needs equality, not proximity.

Concept

This is a one-variable word equation. "Fifth part of N" means N⁄5, and the operations named afterwards act on that part, not on N.

Clearing the fractions first is what keeps the arithmetic clean: multiply every term by the LCM of the denominators, 15, and the equation becomes 3N + 75 = 5N − 105.

The last clause then does its own work. The equation gives N = 90, but the question asks for half the number, so the answer is 45.

Both the number, 90, and its half, 45, are natural things to mark — but only 45 is offered, which is the setter telling you the final clause was the point.

Key facts

The number is 90, and both sides check out at 23: 90⁄5 + 5 = 23 and 90⁄3 − 7 = 23.
"Fifth part of N" is N⁄5, not 5N.
Multiplying by the LCM of the denominators, 15, clears the fractions in one move.

Study next

Word problems whose final demand is a derived quantity — half, twice or the successor of the unknownClearing fractional coefficients using the LCM of the denominatorsTwo-variable statements built from ages, money or digits

Common traps

Solving correctly to N = 90 and then marking the number instead of its half.
Reading "fifth part increased by 5" as (N + 5)⁄5.
Losing a sign when −105 crosses the equals sign.

Linear-equation stems here hide one extra step in the final clause — half the number, twice the number, the larger part.

Read that clause again after solving, because the unknown itself is often not among the options.

Related PYQs

No directly related past PYQ was found.