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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. $21:10:26$
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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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