A man alone can paint a house in 9 day and a woman alone can paint the house in 18 days. If 3 men and 3 women work together, then in how many day they will paint the house?

2 days

One Man’s 1 day work = \(\frac{ 1 }{ 9}\) 

Three men’s 1 day work = 3 x \(\frac{ 1 }{ 9}\) = \(\frac{ 1 }{ 3}\) 

One woman’s 1 day work = \(\frac{ 1 }{ 18}\) 

Three women’s 1 day work = 3 x \(\frac{ 1 }{ 18}\) = \(\frac{ 1 }{ 6}\) 

Three men and three women one day work = \(\frac{ 1 }{ 3}\)  + \(\frac{ 1 }{ 6}\) = \(\frac{ 1 }{ 2}\) 

Three men and three women will complete the work in = 2 days