If the cost of 1m of cloth is Rs. $\frac{1}{3}\times \frac{1}{2}+\frac{1}{3}\times (-\frac{1}{4})$, find the cost of $\frac{9}{11}$ meters cloth.

Cost of 1 m cloth $=\frac{1}{3}\times \frac{1}{2}+\frac{1}{3}\times \frac{-1}{4}$

$=\frac{1}{6}-\frac{1}{12}$

$=\frac{1}{12}$

Hence, the cost of $\frac{9}{11}$ m cloth = $\frac{9}{11}\times \frac{1}{12}=\frac{9}{132}=\frac{3}{44}$ Rs.