A, B and C can complete a piece of work separately in 10, 20 and 40 days, respectively. In how many days will the work be completed if A is assisted by both B and C every third day?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 2)

Answer 1

Given:

A, B and C can complete a piece of work separately in 10, 20 and 40 days, respectively.

A is assisted by both B and C every third day to complete the work.

Concept used:

Total work = Efficiency (Work done per day) × Total time taken

Calculation:

LCM (10, 20, 40) = 40

Let the total work be 40 units.

Efficiency of A = 40/10 = 4 units

Efficiency of B = 40/20 = 2 units

Efficiency of C = 40/40 = 1 unit

In a set of 3 days, total work done = 4 × 2 + (4 + 2 + 1) = 15 units

In such two sets of 3 days, total work done = 15 × 2 = 30 units

For the next 2 days, total work will be done = 30 + 4 + 4 = 38 units

Now, time taken to complete the work entirely = 3 × 2 + 2 + \(\frac {40 - 38}{4 + 2 + 1}\) = \(8 \frac{2}{7}\) days

∴ The work will be completed in \(8 \frac{2}{7}\) days.