At the beginning of 2002, sunil had four dozen goats with him. he increased this stock by x %. at the end of 2002, he sold off y % of his stock. at the beginning of 2003 he again increased his stock by x % and and at the end of 2003, he again sold off y % of his stock. There were no other changes in the number of goats. At the end of 2003 he had five dozen goats with him after his sales which of the following always hold true ?

Question

At the beginning of 2002, sunil had four dozen goats with him. he increased this stock by x %. at the end of 2002, he sold off y % of his stock. at the beginning of 2003 he again increased his stock by x % and and at the end of 2003, he again sold off y % of his stock. There were no other changes in the number of goats. At the end of 2003 he had five dozen goats with him after his sales which of the following always hold true ?

1 - X > 100y / 100 -y

2 - 100y / 100-y > x > y

3 - X < y

4 - 100y / 100-y < x < y

Answer 1

100y / 100-y > x > y

Answer 2

To solve this problem, let's break it down step by step.

Let's first consider the changes that happened in 2002:

Sunil increased his stock by x%. This means he added x% of his initial stock of four dozen goats.

At the end of 2002, he sold off y% of his stock. This means he sold y% of the total stock he had after increasing it.

So, at the beginning of 2003, Sunil had:

4 dozen + (x% of 4 dozen) - (y% of the total stock after the increase) goats.

Now, let's consider the changes that happened in 2003:

Again, Sunil increased his stock by x%. This means he added x% of the stock he had at the beginning of 2003.

At the end of 2003, he sold off y% of his stock. This means he sold y% of the total stock he had after increasing it.

So, at the end of 2003, Sunil had:

(4 dozen + (x% of 4 dozen) - (y% of the total stock after the increase)) + (x% of (4 dozen + (x% of 4 dozen) - (y% of the total stock after the increase))) - (y% of the total stock after the increase).

Simplifying this expression is a bit complicated. However, we can make certain observations.

Since there were no other changes in the number of goats, the final stock is always going to be in dozens. In this case, it is given that Sunil had five dozen goats at the end of 2003.

Now, we can set up an equation to find the values of x and y that satisfy the condition of having five dozen goats at the end of 2003. Let's set up the equation:

(4 dozen + (x% of 4 dozen) - (y% of the total stock after the increase)) + (x% of (4 dozen + (x% of 4 dozen) - (y% of the total stock after the increase))) - (y% of the total stock after the increase) = 5 dozen.

By solving this equation, we can find the values of x and y.

Given the complexity of the equation and the absence of definite values for x and y, it is not possible to determine which of the options always hold true with the given information.