A shepherd has 1 million sheep at the beginning of the year 2000. The numbers grow by x%,(x>0) during the year. A famine hits his village in the next year and many of his sheep die. The sheep population decreases by y% during 2001 and at the beginning of 2002 the shepherd finds that he is left with 1 million sheep. Which of the following is correct?Choices:- y>x x=y x>y xy=0
Question
A shepherd has 1 million sheep at the beginning of the year 2000. The numbers grow by x%,(x>0) during the year. A famine hits his village in the next year and many of his sheep die. The sheep population decreases by y% during 2001 and at the beginning of 2002 the shepherd finds that he is left with 1 million sheep. Which of the following is correct?Choices:- y>x x=y x>y xy=0
Solution
The correct answer is x=y.
Here's why:
Let's denote the number of sheep at the beginning of the year 2000 as S0. So, S0 = 1 million.
At the end of the year 2000, the number of sheep increases by x%. So, the number of sheep at the beginning of 2001 is S1 = S0 * (1 + x/100).
During the year 2001, the number of sheep decreases by y%. So, the number of sheep at the beginning of 2002 is S2 = S1 * (1 - y/100).
According to the problem, S2 = S0 = 1 million.
So, we have the equation S0 * (1 + x/100) * (1 - y/100) = S0.
Solving this equation, we get (1 + x/100) * (1 - y/100) = 1.
Expanding and simplifying, we get x/100 - y/100 = 0, which means x = y.
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