15 men can do a piece of work in 27 days by working 8 hrs a day. But 9 women can do it in 21 days by working 6 hrs a day. Then the ratio of the work done by 1 man and 1 woman is:

27 : 14

Total Work = No. of person × days

Therefore,

Total work ⇒      15M × 27 x 8  = 9W × 21 x 6

                ⇒            M : W       =  \(\frac{9\; \times\; 21\; \times\; 6}{15\; \times\; 27\; \times\; 8}\)

⇒   M : W = 27 : 14