SSC CGL 2025 Tier-I · 16 September 2025, Shift 2 · Quantitative Aptitude · Question 11 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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A, B, and C can complete a certain task in 20, 30, and 60 days, respectively. How many days will it take for A to finish the work if he receives help from B and C every third day?

(a)15 days
(b)12 days
(c)10 days
(d)9 days

Answer

Why

Correct — A. Size the task, then run it in 3-day cycles.

Work = LCM(20, 30, 60) = 60 units
Daily rates: A = 3, B = 2, C = 1 unit

Days 1 and 2, A alone: 3 + 3 = 6 units
Day 3, all three: 3 + 2 + 1 = 6 units
One 3-day cycle = 12 units

60 ÷ 12 = 5 cycles
5 × 3 = 15 days → option (a)

Why the others are wrong

(b)
12 days — 12 days falls short. In 12 days A does 12 × 3 = 36 units, and the help-days 3, 6, 9 and 12 add 4 × 3 = 12, a total of 48 of the 60 units.
(c)
10 days — 10 days is the time if B and C worked every day: 3 + 2 + 1 = 6 units a day, and 60 ÷ 6 = 10. They join only every third day, so it takes longer.
(d)
9 days — 9 days is faster than all three working together every day, which takes 10 days. Help on every third day can only be slower than that.

Concept

Unit work with a repeating cycle. Take the LCM of the individual times as the total work, so each worker's daily output is a whole number.

When help arrives on a fixed pattern, add up one full cycle, divide the total work by it, and multiply by the cycle length.

If the division is not exact, finish the leftover work day by day inside the next cycle, in the order its days fall.

Here the work ends exactly with the fifth cycle: day 15 is itself a help-day, and 5 × 12 = 60, so no part-cycle is needed.

The answer must also lie between 10 days (help every day) and 20 days (A alone), which rules out (c) and (d) before any working.

Key facts

On a 60-unit task, times of 20, 30 and 60 days give daily rates A = 3, B = 2, C = 1.
One 3-day cycle here = 3 + 3 + 6 = 12 units.
Cycles needed = total work ÷ work per cycle = 60 ÷ 12 = 5.

Study next

Alternate-day work, where two workers take turnsWork cycles that finish part-way through a cycleEfficiency ratios: time taken is inversely proportional to daily output

Common traps

Using the combined rate 1⁄20 + 1⁄30 + 1⁄60 = 1⁄10 for every day and answering 10 days.
When the total is not a whole number of cycles, rounding the cycles up instead of finishing the leftover work day by day.

12 Sep 2025, 12:30, Quant Q.12 uses the same frame with a 5-day cycle: rates 3, 2 and 1 on a 90-unit job, B and C join every fifth day, one cycle is 4 × 3 + 6 = 18 units, and 90 ÷ 18 = 5 cycles = 25 days.

Related PYQs

No directly related past PYQ was found.

Topic: Time & Work — all 63 SSC CGL questions on it, every solved shift.