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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:

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SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 4)
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  1.  days
  2.  days
  3.  days
  4.  days

Answer (Detailed Solution Below)

Option 3 :  days
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Detailed Solution

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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 =  

Thus, the time taken to complete the work = 14 days.

∴ The whole work will be completed in 14 days.

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