# Three men can complete a piece of work in 6 days. Two days after they started the work, 3 more men joined them. How many days will they take to complete the remaining work?

1. 4
2. 1
3. 3
4. 2

Option 4 : 2

## Detailed Solution

Given:

Three men can complete a piece of work in 6 days.

Formula used:

$$\frac{M_{1}\ × \ D_{1}}{W_{1}}\ =\ \frac{M_{2}\ × \ D_{2}}{W_{2}}$$

where M= M2 = number of man

D1  = D2 = number of days

W= W2 = part of work

Calculations:

time taken = 6 days

part of work done in 1 day = 1/6

part work done in 2 days = (1/6) × 2 = 1/3

remaining work = 1 - 1/3 = 2/3

so ​​using above formula we get ​

$$\frac{3\ \times\ 2}{\frac{1}{3}}\ =\ \frac{6\ \times\ D_{2}}{\frac{2}{3}}$$

so D2 = 2 days.

∴ the correct answer is 2 days.
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