Multiple choice general knowledge math & puzzles

Farmer Charlie has a chicken farm. On a certain day, Charlie calculates in how many days he will run out of chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.how many chickens he had?

  1. 350

  2. 300

  3. 956

  4. 128
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C be chickens and D be days food lasts. With C-75 chickens, food lasts D+20 days. With C+100 chickens, food lasts D-15 days. Total food F = C*D. So (C-75)(D+20) = (C+100)(D-15) = CD. Solving: CD + 20C - 75D - 1500 = CD + 100D - 15C - 1500. This gives 35C = 175D, so D = C/5. Substituting back and solving yields C=300.

AI explanation

To solve this problem, let's assume that Farmer Charlie initially had "x" number of chickens on his farm.

According to the given information, if he sells 75 chickens, he can feed the remaining chickens for 20 days longer. This means that the amount of chicken food he has can last for (x - 75) chickens for (20 + 15) days.

Similarly, if he buys 100 extra chickens, he would run out of chicken food 15 days earlier. This means that the amount of chicken food he has can last for (x + 100) chickens for (20 - 15) days.

Now, let's set up the equations based on the above information:

Equation 1: (x - 75) * (20 + 15) = x * 20 Equation 2: (x + 100) * (20 - 15) = x * 20

Let's solve these equations to find the value of x, which represents the initial number of chickens.

Expanding the equations: Equation 1: (x - 75) * 35 = 20x Equation 2: (x + 100) * 5 = 20x

Simplifying the equations: Equation 1: 35x - 2625 = 20x Equation 2: 5x + 500 = 20x

Solving for x: Equation 1: 35x - 20x = 2625 15x = 2625 x = 175

Equation 2: 20x - 5x = 500 15x = 500 x = 33.33

Since the number of chickens cannot be fractional, we can conclude that Farmer Charlie initially had 175 chickens on his farm.

Therefore, the correct answer is option A) 350.

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