# Brush up your mind with Anamolies

# Assuming a quantity to be 100

You might have often seen that a quantity is assumed to be 100 in aptitude questions which makes the calculations easy. Can you do that always? In all the questions? If not, then in which cases we do not do so? Keep on thinking.

**Solution:** To understand this, we first need to understand the concept of relative data and absolute data. If we ask a simple question, A and B have money in the ration of 2:3. Can you tell how much money each of them has. No, you cannot. There can be a number of answers for this question, in fact infinite answers. Now, if a question is asked that A has 40% of the total money. Can you tell how much A has or how much B has. Still, not possible. But, if it is given that total money they have is Rs. 5000, the question can be answered easily and uniquely.

The reason is Rs. 5000 is an absolute data. It has a physical significance. Any concrete information like 45 coins, 42 apples, 7 chairs etc. is absolute data. They all have physical significance. But 2:3 or 40% are relative data. They are only relevant only if come with an absolute data. Otherwise, 40% of a quantity can mean anything, it cannot be uniquely defined.

In a question, if you see that all the data given is relative, assume a quantity to be 100 with confidence. You will never get a wrong answer(provided you do other things right). But, if you see even a single absolute data in question, never assume a quantity 100. You may land up with a wrong answer. This was the trick. You can try this on your aptitude questions. If you still are not able to understand, we will be back soon with some examples.

# Discount Series Anamoly

Very often we see on shops and apparel stores, multiple discounts are written like 50%+30%+20% off or 40%+30%+10% discount or in some other way. Does that mean that that we will get a discount of 100% or 80% in the two cases? NO. This is a question that most of us would be able to answer. The question here is that you will nowhere see discounts written in the form 20%+30%+50%. Is it different from 50%+30%+20% or the same or there is some other relation? Putting in simple words, does it make a difference if we write multiple discounts in different order?

**Solution:** Actually, all of these would result in the same discount. You might have studied in your junior classes that the addition is commutative, means a+b+c = b+a+c = c+a+b = ..... .

So, the order in which you add does not make any difference. Same is the case with multiple discount series. The order in which the discounts are calculated does not matter. The end result will always be the same. Let us take an example. If MRP of an item is Rs. 100, and discount series is 50%+30%+20% . After 50% discount, price becomes 50. Then, after 30% discount, price becomes 35, and then after 20% discount, price becomes 28. In other case, If MRP of an item is Rs. 100, and discount series is 20%+30%+50% . After 20% discount, price becomes 80. Then, after 30% discount, price becomes 56, and then after 50% discount, price becomes 28.The final price is same in both the cases.

You can try yourself for other orders as well and figure out if end result is same.