Explanation:

Let's break down the statements:

- Let: Man (M), Woman (W), Boy (B)

- Boy alone finishes work in 20 days ? Boy's 1 day's work = 1/20

- 2 Women together finish work in 30 days ? 2W's 1 day's work = 1/30 ? 1 Woman = 1/60

- Let time taken by (M+W) together = x days, by (W+B) together = 2x days (as stated)

- (M+W)’s 1 day work = 1/x; (W+B)’s 1 day work = 1/(2x)

Set up equations:

- M + W = 1/x

- W + B = 1/(2x)

- We have W = 1/60, B = 1/20

So,

W + B = 1/60 + 1/20 = (1 + 3)/60 = 4/60 = 1/15

So, 1/(2x) = 1/15 ? 2x = 15 ? x = 7.5

Therefore, (M + W)'s 1 day work = 1/x = 1/7.5

So, M + W = 1/7.5 ? M = 1/7.5 - W = (1/7.5) - (1/60)

Let’s take LCM (60): (1/7.5 = 8/60), so

M = (8 - 1)/60 = 7/60

Now, 1 Man’s 1 day work = 7/60

? 4 Men together = 4 × (7/60) = 28/60 = 7/15

Therefore, time to finish work = 1 / (7/15) = 15/7 ˜ 2.14 days

Option 2: 2.14 is correct.

Explanation Summary:

- Calculated individual capacities from statements.

- Derived equations relate capacities of Man, Woman, Boy.

- Found "Man’s" 1 day work, scaled to 4 men.

- 4 men together do work in ~2.14 days.

- Correct Option: Option 2: 2.14 ()