Avi can finish a piece of work in 6 days, Avni can finish it in 8 days, Aarti can do it in 12 days and Reeta can do it in 16 days. They all decided to work one by one, Avi starts the work and works for one-fourth of a day, then Avni works for one-fourth of a day, then Aarti works for one-fourth of a day and then Reeta works for the remaining one-fourth of a day. The cycle is repeated till the work finished. Who was working when the work finished?

Correct option is C

Given:

Avi finishes work in 6 days

Avni finishes work in 8 days

Aarti finishes work in 12 days

Reeta finishes work in 16 days

Each works for one-fourth day in a fixed cycle repeatedly until the work is done.

Formula Used:

Efficiency = $$\frac{\text{Total Work}}{\text{Number of Days}}$$​​

Solution:

Let total work = LCM of (6, 8, 12, 16) = 48 units

Then efficiencies are:

Avi:  $$\frac{48}{6}$$​= 8 units/day 

Avni:  $$\frac{48}{8}$$​ = 6 units/day 

Aarti:  $$\frac{48}{12}$$​ = 4 units/day 

Reeta:  $$\frac{48}{16}$$​ = 3 units/day 

Each works for one-fourth day, so:

Avi’s contribution = $$8 \times \frac{1}{4}$$​ = 2 units

Avni’s contribution = $$6 \times \frac{1}{4}$$​ = 1.5 units

Aarti’s contribution = $$4 \times \frac{1}{4}$$​ = 1 unit

Reeta’s contribution = $$3 \times \frac{1}{4}$$​ = 0.75 unit

Total work per cycle (1 full day of 4 one-fourth parts):

= 2 + 1.5 + 1 + 0.75 = 5.25 units per cycle

Now,  total work by per cycle contribution:

$$\frac{48}{5.25}$$​ = 9 cycles  + $$\frac{3.75}{5.25}$$ = 9 cycles + $$\frac{5}{7}$$​​

Work done in 9 full cycles =  9 × 5.25 = 47.25 units

Remaining work = 48 - 47.25 = 0.75 units

Next cycle order: Avi → Avni → Aarti → Reeta

Avi works for one-fourth day = 2 units → work still remaining: 0.75 → so Avi alone finishes