The CAT Math sample question for the day is from the topic Percentages in Arithmetic .
Question:
A shepherd has 1 million sheeps at the beginning of 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 sheeps 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 sheeps. Which of the following is correct?
- x > y
- y > x
- x = y
- Cannot be determined
Solution:
Let us assume the value of x to be 10%.
Therefore, the number of sheep in the herd at the beginning of year 2001 (end of 2000) will be 1 million + 10% of 1 million = 1.1 million
In 2001, the numbers decrease by y% and at the end of the year the number sheep in the herd = 1 million.
i.e., 0.1 million sheep have died in 2001.
In terms of the percentage of the number of sheep alive at the beginning of 2001, it will be (0.1/1.1)*100 % = 9.09%.
From the above illustration it is clear that x > y.
