The number of hens, ducks and goats in farm $P$ are $65,91$ and $169,$ respectively. The total number of hens, ducks and goats in a nearby farm $Q$ is $416.$ The ratio of hens : ducks : goats in farm $Q$ is $5:14:13.$ All the hens, ducks and goats are sent from farm $Q$ to farm $P.$

The new ratio of hens : ducks : goats in farm $P$ is ________

1. $5:7:13$
2. $5:14:13$
3. $10:21:26$
4. $21:10:26$

First we can calculate the number of hens, ducks and goats in farm $Q.$

• Number of hens in farm $Q = \dfrac{5}{32} \times 416 = 65$
• Number of ducks in farm $Q = \dfrac{14}{32} \times 416 = 182$
• Number of goats in farm $Q = \dfrac{13}{32} \times 416 = 169$

Initially, the number of hens, ducks and goats in farm $P$ are $65,91$ and $169$ respectively.

All the hens, ducks, and goats are sent from farm $Q$ to farm $P.$

Therefore, in farm $P,$

• Number of hens $= 65 + 65 = 130$
• Number of ducks $= 91 + 182 = 273$
• Number of goats $= 169 + 169 = 338$

$\therefore$ The required ratio $= 130:273:338 = 10:21:26$

So, the correct answer is $(C).$

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