### Percentages, fractions : Quant Practice Problem - Arithmetic : Ascent Education : TANCET, XAT Coaching

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# Percentages - Quant/Math - TANCET 2016, XAT 2016 Practice

The Math sample question 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?
1. x > y
2. y > x
3. x = y
4. Cannot be determined

(x > y). Choice (1)

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.