A farm has chickens, rabbits, and guinea pigs. 25% of the animals are chickens, 30% are rabbits, and the rest are guinea pigs. If the number of chickens doubled, what percentage of the total animals would be guinea pigs?

1. Problem Description

A farm has chickens, rabbits, and guinea pigs. 25% of the animals are chickens, 30% are rabbits, and the rest are guinea pigs. If the number of chickens doubled, what percentage of the total animals would be guinea pigs?

2. Solution Steps

Let $C$ be the percentage of chickens, $R$ be the percentage of rabbits, and $G$ be the percentage of guinea pigs.

Initially, $C = 25\%$, $R = 30\%$.

Since the percentages must add up to 100%, we have

$C + R + G = 100\%$

$25\% + 30\% + G = 100\%$

$55\% + G = 100\%$

$G = 100\% - 55\% = 45\%$

Now, the number of chickens doubles. The new percentage of chickens $C'$ is $2 \times C = 2 \times 25\% = 50\%$.

The percentage of rabbits remains the same, so $R = 30\%$.

Let $G'$ be the new percentage of guinea pigs.

Then $C' + R + G' = 100\%$

$50\% + 30\% + G' = 100\%$

$80\% + G' = 100\%$

$G' = 100\% - 80\% = 20\%$

However, note the number of chickens doubled while the total number of animals on the farm remains constant. So, if we denote the original number of animals as $N$, we had $0.25N$ chickens, $0.30N$ rabbits and $0.45N$ guinea pigs.

If the chickens doubled their number, now we have $0.50N$ chickens, $0.30N$ rabbits, and guinea pigs should have been reduced so that the overall total still remains as $N$.

So the new number of guinea pigs are calculated as

$N = 0.50N + 0.30N + \text{New Guinea Pigs}$

$N = 0.80N + \text{New Guinea Pigs}$

$\text{New Guinea Pigs} = N - 0.80N = 0.20N$

Therefore the percentage of the new guinea pigs is equal to $0.20N/N = 20\%$, which is wrong.

The error in our previous reasoning comes from the assumption that the number of animals remains constant. In fact, the total number of animals is increased if the chickens number doubles. Let us denote the initial number of animals as $N$. Chickens make up $0.25N$, rabbits make up $0.30N$ and guinea pigs make up $0.45N$. Then $0.25N+0.30N+0.45N=N$.

Now the number of chickens doubles. The new number of chickens is $2(0.25N)=0.5N$. The number of rabbits remains the same, so it is still $0.3N$. The number of guinea pigs remains also unchanged, so it is still $0.45N$. The new total number of animals $N'$ is $0.5N+0.3N+0.45N = 1.25N$.

Then the new percentage of guinea pigs is given by the fraction $\frac{0.45N}{1.25N} = \frac{0.45}{1.25} = \frac{45}{125} = \frac{9}{25} = \frac{36}{100} = 36\%$

3. Final Answer

B) 36%