# The number of chickens to the number of ducks on a farm was 6: 5. After 63 ducks were sold, there were 3 times as many chickens as ducks left. How many chickens and ducks were there altogether on the farm in the end?

Total chickens and ducks in the end are $168$ in number.
Let $6 x \mathmr{and} 5 x$ be the numbers of chickens and ducks were on the farm. After $63$ ducks were sold , remaining ducks were $\left(5 x - 63\right)$ are in number.
Now by condition , $6 x : \left(5 x - 63\right) = 3 : 1 \mathmr{and} \frac{6 x}{5 x - 63} = \frac{3}{1} \mathmr{and} 6 x = 15 x - 189 \mathmr{and} 9 x = 189 \mathmr{and} x = \frac{189}{9} = 21$
Total number of chickens and ducks in the end are $\left(6 x\right) + \left(5 x - 63\right) = 11 x - 63 = 11 \cdot 21 - 63 = 231 - 63 = 168$ in number.[Ans]