Formula For Mean

In previous post i wrote all about  Arithmetic Progression, Geometric Progression & Harmonic Progression

Different Mean  are 

Arithmetic Mean(AM)

Geometric Mean (GM) &

Harmonic Mean(HM)

Formulas For All Are->

For Two Number a and b .......................

Arithmetic Mean(AM)

AM=(a+b)/2 

 Geometric Mean (GM) 

GM=√ab

Harmonic Mean(HM) 

HM=2ab/(a+b)

Arithmetic Progression-Concept And Formula-Quant

Readers ,our today topic isProgression(series)


First of all 
Progression is nothing but series, in which numbers are arranged in some pattern.


Progression  has 3 types
1)Arithmetic Progression
2)Geometric Progression
3)Harmonic Progression

 

We start with  Arithmetic Progression

Define :  
If Difference of any two consecutive number in the series  is called Arithmetic Progression
Series is a,a+d,a+2d,......a+(n-1)d


         a=first term in the series
         d=difference of consecutive number

Ex.2,5,8,11.....

Formulas:

->If we want to find nth term in this progression , formula is tn=a+(n-1)d
here
      tn=nth term in the series
      a=first term in the series
      d=difference of consecutive number

->If we want to find the Summation of all number of series, then formula is 
      Sn=n/2[2a+(n-1)d]
       
      where,
      Sn=Summation Of all number in the series
      a=first term in the series
      d=difference of consecutive number 
      n=total member in the series

->If we know the first term and last term in this series then Summation Formula is easy
that is  Sn=n(a+l)/2
          
          where,

         Sn=Summation Of all number in the series 
       a=first term in the series
        l=last number in the series
        n=total member in the series
      

Geometric Progression

Define :
If ratio of any two consecutive number in the series  is called Arithmetic Progression
Series is a, a*r, a(r^2), a(r^3),a(r^4),a(r^5).....,a(r^n)

            a=first term in the series
            r=ratio of two consecutive number


Formulas:
->If we want to find nth term in this progression , formula is tn=a*(r^ n-1)
here
      tn=nth term in the series

      a=first term in the series
      r=ratio of two consecutive number

->If we want to find the Summation of all number of series, then formula is 
      Sn=a(1- r^n)/(1-r)    if r<1
       Sn=a(r^n -1 )/(r-1)    if r>1
   
      where,
       Sn=Summation Of all number in the series

       a=first term in the series
        r=ratio of two consecutive number 

        n=total member(number) in the series

->In this series if infinite number is available
   then Summation is
          
       Sn=a/(1-r) where -1<r<1

       

Harmonic Progression

Define :
If numbers' reciprocal is in the Arithmetic Progression, then series of number is called Harmonic Progression

Series is 1/a , 1/(a+d) , 1/(a+2d) , 1/(a+3d),........

Formulas:
->To find the nth term of this series
you should find nth term of corresponding arithmetic progression and then reciprocal of that. 

if series is 1/2 , 1/4 , 1/6 .... then 

to find n th term first we find nth term of 2,4,6....
then reciprocal of it is nth term of Harmonic Progression.

I hope this post will help to understand the topic of Progression
Our next topic will be on Median 
thank U.


 

Profit & Loss-Concept Quant

Profit & Loss




To understand above two terms first we should understand three important terms
   that are
                  cost price
                       market price and
                       sales price
                 

Cost price:-total cost to make the product[total cost incurred by the person in acquiring product]

Market Price:-market price is nothing but price which is labelled on the product or quoted

Sales Price:-Sales Price is nothing but,price of actual transaction

here one important term take place that is discount

Discount:- Some rupees are reduced by Sellers is discounts to customer.

Relations

1)Discount=Selling Price-Market Price

2)Discount is always calculated on the basis of market price(Remember)

Now ,About Profit & Loss

Profit:- If Selling price is higher than cost price, difference of them is called Profit

Loss:- If Selling price is lower than cost price, different of them called as Loss.

Formulas:-

1)Profit=Sales Price-Cost Price

2)Loss=Cost Price-Selling Price

3)Discount=Market Price-Selling Price

4) Profit(in %)=

[(Selling Price-Cost Price)/CostPrice]*100

5)Loss(in %)=

 [(Cost Price-Selling Price)/Cost Price]*100

If any query regarding any posts,then mail on crackaptitude@gmail.com

Thanks...

 

 

 

                   

 

Boats And Streams Concept & Formula

Boats And Streams Concept=>

We can assume 2 objects in the stream

that is 

1)stationary object(which is run at stream's speed)

2)Moving object(which is run at stream's speed+its own speed)

In 2nd case Either object move in the direction of object or opposite direction of stream

A)In the Direction Of Stream(Called Downstream)

B)In the Opposite direction Of Stream( Called Upstream)

If x is the speed of a bot(in still water)

and y is the speed of the stream

Formula for

downstream a=x+y and

upstream     b=x-y

From Above two formula 

        x=(a+b)/2

        y=(a-b)/2

In Short,

Speed Of the boat in still water=x=(downstream speed+upstream speed)/2

And

Speed Of the Stream=y=(downstream speed-upstream speed)/2

I think It may be helpful to U....Thanks

Quant-Cost

A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:
a) Rs. 456
b) Rs. 458
c) Rs. 558
d) Rs. 568

 

sol>

Here l=25m,b=12m and h=6m

so for 

2walls area is 2*[length*height]=2*[25*6]=300Sq.m

another 2 walls area is =2*[width*height]=2*[12*6]=144Sq.m

for 1 wall which is base , area is=25*12 =300Sq.m

 

sum of their area is =300+300+144=744

Now for plastering of 1 side cost is 75paisa= .75 rs

then for our area cost=.75*744 =558

 

is the ans.

 

 

Quant-Calculate Squares

Calculate Squares

sol>4+1+4+1+1

=11 is the ans

Quant Permutation and Combinatiopn

There are 10 Points on a one straight line and 11 points on another straight lines... How many different types of triangles can be formed using these points as a vertices ??

 

sol>Here 2 Cases possible

1)take 1 point from the line which contain 10 points, and now we have to select 2 points from the other line so

2) take 1 point from the line which contain 11 points and now we have to select 2 points from the other line so

Case 1:

11C2 = 55

now 10 such possibilities so 55 X 10 = 550

case 2:
10C2 = 45

now 11 such possibilities so 45 X 11 = 495

hence total = 550 + 495 = 1045

is the ans 

Quant-Triangle Calculation

Calculate Triangles:

Sol->

Ans is 27

you can do manually or by formula

n(n+2)(2n+1)/8 if n=even

n(n+2)(2n+1)-1/8 if n=odd

small traingles at the base of big traiangle..

so

n=4

=[4(4+2)(2(4)+1)]/8

=216/8

=27

is the ans.

Quant

unit digit of 723^723  *  824^824   *  529 ^529 ?????????????

 

sol>

723^723=723^720 * 723^3 term will gve last digit .........7 ......... (1*7)
824^824=824^820 * 824^4 term will gve last digit........6.............(4*4)
529 ^529=529 ^520 * 529 ^9 term will gve last digit.......9...............(1*9)

then
7*6*9=unit digit 8

Quant

ANSWER THIS IF YOU CAN!!
- you enter a bus
- in that you see 7 girls
- each girl has 7 bags
- in each bag there are 7 big cats

- each big cat has 7 small cats
- each cat has 4 legs
Calculate the no of legs in the bus.....

 

sol>

Each big cats have 7 small cats. Systematically, 7 small cats has 28 legs (7 * 4) combined with the big cat that owns this 7 small cats.Let's call this the "cat chain", so cat chain 1 has 32 legs altogether. So since there are 7 big cats 7 * 32 = 224 legs. Therefore each backpack has 224 legs. Finally, each girl has 7 * 224 = 1568 legs. Lastly, since there are 7 girls, A to G, there are 7 * 1568 legs (per girl) = 10976 legs.Now, since each girl also has 2 legs each and your 2 legs;SO, (7 * 2) + 2 + 10976 = 10992 legs altogether

Time And Distance

A and B are traveling from a distance X and Y. A starts at 12p.m at a speed of 6km/hr and B starts at 1.30p.m at a speed of 8km/hr. At what time will be the 3 km ahead of A.
a) 3p.m
b) 4.30p.m
c) 6p.m
d) 7.30p.m

sol> 

A start 12 pm 6+6+6+6+3 = 27 km cover at 4:30
B start 1 :30 4+8+8+4 =24 km at 4 30...

Logic

There are 60 slots around a circle, numbered from 1 to 60. A man starts from the 1st slot then 5th slot and jumps into the 9th slot and so on. In which slot will he land in his 2200th jump?
a) 45
b) 41
c) 1
d) 5

 

sol>

in each 15 jump he will complete circle.............so at 2190step he will on 1st slot.................................in remaining 10 jump he will on 45th slot.////////////////////

Pipe and tank

Three pipes A,B,C can fill a tank in 6 hrs.After working together for 2 hrs, C is closed and A & B can fill the remaining in 7 hrs.The number of hrs taken by C alone to fill the tank is
a.10
b.12
c.14
d.16

spl>

1/a + 1/b +1/c = 1/6..now in 2 hrs they'l cmplt 1/3 wrk.so the remaining 2/3 wrk is dne in 7 days.so whole wrk by a and b is done in 10.5 days.so 1/a + 1/b=2/21..by solvn 2 eqn we get c=14.

Series

Find the missing numbers in the series: 0,2,5,?,17,28,?,

sol>

0, 0+2, 2+3, 5+5, 10+7, 17+11, 28+13
2,3,5,7,11,13 these are prime numbers

Arrangement

There r 3 boys & 4 girls; How many ways they r arranged such that boys should be always together ???

 

sol>

4 girls + 1 boy unit(all 5 together) . so 5! * ( 3 boys can be arranged in 3! ways) => 5!*3!

Series

FIND THE ODD ONE
331,482,551,263,383,242,111

 

sol>

383

 here odd doesn't mean odd numbers...

2nd digit of no.=1st digit no.* 3rd digit no.

Logic image

sol>b..only b does not contain any repetitions

Logic Fig

Which symbol will be on the face opposite to the face with symbol * ?

A. @ B. $
C. 8 D. +

 

sol>

from 1st figure you can see that "@" and "-" can not be opposite to "*". From 2nd figure its seen that "+" can also not be opposite to "*". From 3rd figure its seen that "$" can also not be opposite to "*". Hence only "8" is opposite to "*".

 

Logic

Introducing a boy, a girl said, "He is the son of the daughter of the father of my uncle." How is the boy related to the girl?

A. Brother B. Nephew
C. Uncle D. Son-in-law

 

sol>brother

Logic

A man is wearing black. Black shoes, socks, trousers, lumper, gloves and balaclava. He is walking down a black street with all the street lamps off. A black car is coming towards him with its light off but somehow manages to stop in time. How did the driver see the man?

 

sol>its day time

 

discount

A shopkeeper gives 12% additional discount on the discounted price, after giving an initial discount of 20% on the labeled price of a radio. If the final sale price of the radio is Rs.704, then what is its labeled price?

 

sol>

1000rs. Sale price=(1-discount1)(1-discount2)....(1-discountn)market price.