A and B can complete a piece of work in 13 and 17 days respectively. A begins to do the work, and they work alternatively one at a time for one day each. The whole work will be completed in:

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 4)
View all SSC CGL Papers >
  1. \(17\frac{{11}}{{17}}\) days
  2. \(17\frac{{17}}{{19}}\) days
  3. \(14\frac{{11}}{{17}}\) days
  4. \(11\frac{{11}}{{17}}\) days

Answer (Detailed Solution Below)

Option 3 : \(14\frac{{11}}{{17}}\) days
super-pass-live
Free
SSC CGL Tier 1 2025 Full Test - 01
3.3 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

Given:

Time in which A can complete a piece of work = 13 days

Time in which B can complete a piece of work = 17 days

Concept used:

L.C.M. of 13 and 17 = 221

Thus, total work done = 221 units.

Unit of work done by A in 1 day = 17 units

Unit of work done by B in 1 day = 13 units

Calculation:

If A and B work alternatively, work done by them in 2 days = 30 units

Work done in 14 days = 30 × 7 = 210 units

Work left = 11 units

Work done remaining by A on 15th day = \(11 \over 17\) 

Thus, the time taken to complete the work = 14\(11 \over 17\) days.

∴ The whole work will be completed in 14\(\bf 11 \over 17\) days.

Latest SSC CGL Updates

Last updated on Jul 9, 2025

-> The SSC CGL Notification 2025 for the Combined Graduate Level Examination has been officially released on the SSC's new portal – www.ssc.gov.in.

-> Bihar Police Admit Card 2025 Out at csbc.bihar.gov.in

-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.

-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.

->  Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.

-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.

-> The CGL Eligibility is a bachelor’s degree in any discipline.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

-> The AP DSC Answer Key 2025 has been released on its official website.

-> The UP ECCE Educator 2025 Notification has been released for 8800 Posts.

More Work Efficiency Questions

More Time and Work Questions

Get Free Access Now
Hot Links: teen patti all games teen patti octro 3 patti rummy teen patti gold new version teen patti bindaas teen patti noble