Sometimes,we are in great hurry because of which we make very simple mistakes and we do not know. Making a mistake is one thing and being unaware of the mistake being done is yet another.

Now I will show you where a large number of students make mistake in questions of percentage.

Problem : If x is 25% more than y. Then how much is y less than x expressed as % of x.

Solution: As soon as the question is read, a majority gives the answer y is 25% less than x. Second category of people those who will see it as a trick and they will take two simple numbers. x=100 and y =75

So that x is 25 more than y. Here they fail to realize the term percentage. so they will also end up saying y is 25 less than x, hence answer is 25%.

But the answer to it must be solved for you now

X is 25% more than y

say y = 100

so x = 125

Talking in Percentage % change (incraese than y) in x = 25 % as per question = (x-y) / y = (125-100)/100 = .25 or 25%

Now similarly % change (decrease than x ) in y = (y-x) / x = (100-125)/125 = - 25/125 = -1 /5 = -0.2 or -20%

-ve sign indicates the decrease w.r.t. x

Hence the answer must be y is 20% less than x.

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