10 men or 15 women can complete a work in 30 days. In how many days can 15 men and 27 women complete the work?

$9\frac{1}{11}$

10 Men = 15 Women,

Men : Women = 15 : 10 = 3 : 2 (Efficiency)

⇒ Total work = 10(3) x 30 days = 30 x 30 = 900 units,

⇒ Time required by 15 Men and 27 Women to complete the total work = \(\frac{900}{15(3)+27(2)}\) = \(\frac{900}{99}\) = \(\frac{100}{11}\) = \( {9 }_{11 }^{ 1} \) days.     ..(\(\frac{Work}{Efficiency}\) = Time)