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Type of numbers

Type of Numbers

Remainders....

Remainders theory

Factor theory...

Factors Theory

Logic Funda

• The 20 digit number 1920212223….2728, was obtained by listing the integers from 19 to 28. 10 digits of this number are now removed, so that the resulting number is as large as possible. What are the first 3 digits of the new 10- digit number?

A.942
B.967
C.956
D.989
E.999

AVERAGE

Average has a great significance in BANK PO. Not only in Math's but in DI section also, Average based questions are coming. I am writing this topic in layman's language. So that back-benchers also can understand. Everybody knows the meaning of average which says:

AVERAGE= Sum of observation / no. of observation

Now come to the practical meaning. Let me start with examples;

• 5 students are sitting in a room. They have average money of 45 Rs. 'A' goes out. Now the average money becomes 44 Rs. How many Rs. does 'A' have?
  

Ans. Firstly, if average money with 5 students is 45 Rs. It does not mean that every student has 45 Rs. It means, if they were having same money, then amount would have been 45 Rs. with each student. In total, they have 45x5 Rs.

Now answer to the question…one way to ans. Is:

45x5-44x4=49  

I am sure most of the students have done in this way only.

But why to calculate, if the sum can be damn easy by logic.

Smart Application:
Suppose every student has 45 Rs. in his pocket. If A were taking 45 Rs, there would have been no change in the amount of rest of the students. But since average falls by 1 Re. It means remaining 4 persons (except A) have 1 Re. less. In total 4 Rs. are missing. Where are these 4 Rs.? Obviously with A, because he is taking his own 45 Rs. + 4 Rs. = 49 Rs.  

Now try to solve following questions by using your brain. You are not allowed to write….

• Average weight of 10 men is 50 kg. Sanjay joins the group and average becomes 51 kg. What is weight of Sanjay?
  

Think this way:
Average money with 10 men is 50 Rs. Sanjay comes in and average becomes 51 Rs. What amount does Sanjay has?

If Sanjay were coming with 50 Rs., there would have been no change. Since, there is a rise of 1 Re. per head and there are 11 persons in the new group. It means Sanjay has come with 11 Rs. more. So Ans. = 50+11=61 Rs.  

• The average weight of class of 40 students is 50 kg, while the average weight of class along with Fatty and Motu is 51 kg. What is the average weight of Fatty and Motu?
  

Again be money minded….

40 students have 50 Rs. each. 2 persons are coming. Suppose they had entered with 50 Rs. each (100 Rs. In total), there would have been no change. But there is rise of 1 Rs. per head. (Now 42 students in total)

=1x42 in total

=Amount with Fatty and Motu = 100+42=142 Rs.

Average amount = 142/2= 71 Rs.  

• In the 15th inning, Sachin scored 58 runs. Thereby decreasing his average by 3 runs. What is his new average?
  

  Or
  

• A group of 14 persons has certain average money. A new student joined the group with 58 Rs. Thereby decreasing average by 3 Rs. What is the new average of the group?
  

By Equation:-

Let the old average be x

(14x+58)/15=(x-3)

=14x +58= 15x-45

= x=103

So, new average= 103-3=100  

Now we will do it as done earlier. Since the fall in average (of 15 students) is 3. i.e. every student is short of 3 Rs. It means in total, group is losing 3x15=45 Rs. Where are these Rs? Of course with new student. He came with 58 Rs. Of his own+ he stole 45 Rs from the group i.e. = with 103 Rs. = old average of the group. But average fall by 3. So new average is 100.  

• Group A of 45 students has average weight 25 kg.
  

  Group B of 30 students has average weight 26 kg.
  

  What is the combined/pooled average of both these group?
  

We will think this way… (Again Monetary approach)

If every student of group B was carrying 25 Rs, then the pooled average would have been 25 Rs. Only. But now group B's students are coming with extra 1 Rs. Per head i.e. 30 Rs. In total. These 30 Rs we will divide equally among 45+30 students. So, each student's additional share will become 30/75 Rs. So, new average 25+30/75=25.4 Rs. Ans.  

• What is average of 1, 2, 3… 49?
  

Average of n Consecutive natural no.= (n+1)/2

So, there average is = (49+1)/2=25                          

Or average is nothing but middle no. (if terms are in A.P )

• On a blackboard, 76 consecutive numbers (starting with 1) were written. Yogesh come and deleted 27. What is the average of remaining numbers?
  

Average of 1,2,3,….,76=(76+1)/2 = 38.5  

(Now again this sum boils out in Money sum.)

76 persons have average money 38.5 Rs. 1 person with 27 Rs. goes away. What is average of remaining group? Yogesh is taking 27 Rs. out of 38.5 Rs. It means he is leaving 38.5-27=11.5 Rs. for the group. Rest of the 75 people equally divides this sum and new average will become 38.5+ (11.5/75).

Suppose in the above example, we have deleted 70. Now what will be the change in average?

Now instead of 38.5 Rs., the money stealer is going with 70 i.e. 31.5 Rs. extra. So, these 31.5 Rs. should be taken from remaining 75 persons. So,

New Average = 38.5-

         =38.5-0.42

         =38.08  

• Always remember:
  

1. If x is added in all items, then average increases by x.
   
2. If x is subtracted in all items, then average decrease by x.
   
3. If every item is multiplied by x, then average also gets multiplied by x.
   
4. If every item is divided by x, then average also gets divided by x.
   

 

I guess now you can relate all the above fact with many (monetary) things. Now it's your turn to turn & churn your mind wheel. I am giving you a practice exercise that, I am a damn sure, if you will do with sincerity, you will never stuck in average funda.