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X alone can finish a work in 18 days, Y alone can finish the same work in 9 days. If X, Y and Z together can finish the same work in 4 days, then in how many days Z alone can finish the work?

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SSC MTS (2022) Official Paper (Held On: 18 May, 2023 Shift 1)
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  1. 12 days
  2. 10 days
  3. 14 days
  4. 16 days

Answer (Detailed Solution Below)

Option 1 : 12 days
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Detailed Solution

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Given:

X alone can finish a work = 18 days

Y alone can finish a work = 9 days

(X + Y + Z) together can finish the work = 4 days

Formula used:

Total work = efficiency × time

Calculation:

Efficiency Person Time Total work
2 X 18 36
4 Y 9
9 X + Y + Z 4

Now,

⇒ X + Y + Z = 9 units

⇒ 2 + 4 + Z = 9

⇒ 6 + Z = 9

⇒ Z = 3 units

Z alone can finish the work = 36/3 = 12 days

∴ The correct answer is 12 days.

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Latest SSC MTS Updates

Last updated on Jul 14, 2025

-> The IB ACIO Notification 2025 has been released on the official website at mha.gov.in.

-> SSC MTS Notification 2025 has been released by the Staff Selection Commission (SSC) on the official website on 26th June, 2025.

-> For SSC MTS Vacancy 2025, a total of 1075 Vacancies have been announced for the post of Havaldar in CBIC and CBN.

-> As per the SSC MTS Notification 2025, the last date to apply online is 24th July 2025 as per the SSC Exam Calendar 2025-26.

-> The selection of the candidates for the post of SSC MTS is based on Computer Based Examination. 

-> Candidates with basic eligibility criteria of the 10th class were eligible to appear for the examination. 

-> Candidates must attempt the SSC MTS Mock tests and SSC MTS Previous year papers for preparation.

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