A and B alone can do a piece of work in 4 and 9 days, respectively. In how many days will the work be completed, if they both work on alternate days, starting with B? 

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SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 2)
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Given:

A can do a piece of work = 4 days

B can do a piece of work = 9 days

Formula used:

Total work = efficiency × time

Calculation:

Efficiency Person Time Total work
9 A 4 36
4 B 9

Now,

(B + A) = 4 + 9 = 13 units = 2 days

⇒ (13 × 2) = 26 units =  (2 × 2) = 4 days

⇒ 30 units = 5 days

⇒ 36 units = 5 + (6/9) = 5 days

∴ The correct answer is 5 days.

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