A and B can individually complete a piece of work in 18 days and 30 days, respectively. A and B started working together, but A left \(16\frac{2}{3}\) days before the work is completed and B alone completed the rest of the work. For how many days did A work?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 1)

Answer 1

Given:

A and B can individually complete a piece of work in 18 days and 30 days, respectively.

A and B started working together, but A left \(16\frac{2}{3}\) days before the work is completed

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day

Calculation:

Let, after x days work completed

Let the total work is the 90 units (LCM of 30 and 18)

Efficiency of A is 90 / 18 = 5 units

Efficiency of B is 90 / 30 = 3 units

As per the question,

5 × (x - 50/3) + 3x = 90

⇒ 8x = 90 + 250 /3

⇒ 8x = 520/3

⇒ x = 65/3

A work for 65 /3 - 50/3 = 5 days

∴ The correct option is 2

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