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True Discount and Banker's Discount problems tricks in Hindi | fast track formulae for problem solving.

TRUE DISCOUNT AND BANKER'S DISCOUNT TRICKS IN HINDI

TRUE DISCOUNT 1). वास्तविक बट्टा = मिश्रधन - वर्तमान धन
2). यदि ब्याज की दर r% वार्षिक , समय t व वर्तमान धन (pw) है, तो वास्तविक बट्टा = PW×r×t/100
3). यदि r% तथा समय t के बाद देय धन A है, तो तत्काल धन pw = 100×A/(100+r.t)
4). यदि देय धन A पर r% व समय t दिए गए है, तो वास्तविक बट्टा = A.r.t /(100+r.t)
5). यदि किसी निश्चित समय के पश्चात निश्चित वार्षिक दर पर, देय धन पर वास्तविक बट्टा (TD) व समान समय व दर के लिए साधारण ब्याज (SI) हैं, तो देय धन A =      SI × TD/(SI - TD)
6). यदि t समय पश्चात r% वार्षिक दर पर, देय धन पर वास्तविक बट्टा (TD) व साधारण ब्याज (SI) है , तो -  SI - TD = TD×r×t/100
7). t वर्ष बाद r% चक्रवृद्धि दर पर देय धन A का तत्काल धन (PW) = A/(1+r/100)^t   व वास्तविक बट्टा = A - PW
BANKER'S DISCOUNT1). महाजनी बट्टा = शेष समय (समाप्त न हुए समय) के लिए बिल पर ब्याज = बिल की राशि × दर × शेष समय /100
2). महाजनी लाभ = महाजनी बट्टा - वास्तविक बट्टा
3). यदि बिल का मान / अंकित मूल्य A है, समय t व दर r% है, तो महाजनी बट्टा = A×r×t/100
4).…

AVERAGE Problems tricks | fast track arithmetic formulae for problem solving. for all competitive examination//

Today in "laws of nature" we are going to talk about the very important arithmetic formulae on AVERAGE , which are very helpful for all types of competitive examination.

AVERAGE PROBLEM SOLVING TRICKS


1). If the number of the quantities and it's sum is given then the average is given by = sum of the quantities/no. of the quantities

2). If the no. of the quantities and it's average is given then the sum of the quantities is = no. of the quantities × it's average.

3). If the sum and it's average is given then the the no. of the quantities is = sum of the quantities/ average

4). If the average of A boys is x , and the average of B girls is y, if all of them is put together , then average is = (Ax + By)/(A+B)

5). If average of A boys is x , and average of B boys out of A boys is y then average of rest boys is = (Ax-By)/(A-B)

6). If the average of A objects is x , if any object is removed from the list then average become y then the magnitude of removed object is =A(x-y)+y

7). If the average of A no. is a , if x is added or subtracted from each no. then the average become = (a+x) if added or (a-x) if subtracted.

8). If average of A quantities is x , and if a new quantity is added then average become y, then the added new quantity is =A(y-x)+y

9). If the average of A no. is x , then if each no. is multiplied or divided by y then , the average become = xy if multiplied or x/y if divided.

10). If the average weight of A person is increased by x kg if one person of weight y kg is replaced by a new person , then the weight of new person is = y + Ax
*If average is decreasing then the weight of new person is = y- Ax

11). The average marks obtained by A candidates in a certain examination is m, if the average marks of passed candidate is n, and the fail candidate is o, then the no of candidates who passed the exam is =
[A(m-o)/n-o] and no of candidates who failed the exam is =[A(n-m)/n-o]

12). If average of n no. is 'a' , (where n is odd no.) And average of first (n+1/2) no. is 'b' and
Last (n+1/2) no. is 'c' then the  (n+1/2)th no. is = [(n+1/2)(b+c) - na]

13). If a batsman in n innings makes a score of x , and average is increased by y, then average after n innings is = [x-y(n-1)]

14). If a batsman has average of x runs after the completion of n innings. Then no of runs he has to make to raise his average to y is =
[n(y-x)+y]

15). If a person travels a distance with x km/h , and again travels the same distance with y km/h, then average speed for whole journey is = 2xy/x+y km/h

* If half of the distance is travelled by x km/h and other half distance is travelled by y km/h then average for whole journey is =
  2xy/x+y km/h

* If person goes with x km/h and return with y km/h then average speed is = 2xy/x+y km/h

16). If a person travels three equal distances with x km/h , y km/h and z km/h then average speed for whole journey is =
         3xyz/xy+yz+zx km/h

17). If a person travels A km by x km/h, B km by y km/h and C km by z km/h then average speed for whole journey is =

18). A person travels Ath part of a distance with x km/h , Bth part of distance with y km/h, and Cth part with z km/h then average speed for whole journey is =
                                       1/(A/x +B/y + C/z). Km/h

* If Ath, Bth and Cth part of distance is given as A%, B% and C% then formula change to average speed of = 100/(A/x + B/y + C/z) km/h

19). The average value of all the members of a group is x, if the first part of members has average of y, and average of remaining parts of members is z and no. of members in first part is n then no. of members is remaining part =[n(x-y)/z-x]

* If n is the no. of members in remaining part then the no. of members in first part is =[n(x-z)/y-x]

20). The average of first n natural number is = n+1 /2

21). The average of n consecutive number is the middle no. ( Where n is odd number).

22). Average of n consecutive number is the average of middle two numbers. ( Where n is even number).

* The average of two middle number is calculated as follows:
** In case of consecutive numbers,
 Average = smaller middle no. +0.5 or greater middle number -0.5
** In case of consecutive odd and consecutive even.
  Average = smaller middle no. +1 or greater middle no. -1
   

23). The average of odd number from 1 to n, (where n is natural odd number) is =last odd number +1 /2

24). The average of even number from 1 to n, (where n is natural even number) is = last even number +2 /2

25). The average of square of natural number till n is = [(n+1)(2n+1)/6]

26). The average of cubes of natural number till n is = [n(n+1)^2/4]

27). The average of first n consecutive even number is =n+1

28). The average of first n consecutive odd number is =n

29). The average of squares of first n consecutive even number is =
                                                    [2(n+1)(2n+1)/3]

30). The average of squares of even number till n is =[(n+1)(n+2)/3]

31). The average of squares of consecutive odd number till n is =[n(n+2)/3]

32). The average of n numbers is A , and rechecking it is find that some of the numbers that is (x1 , x2, x3, ...xn) are taken wrongly as ( x1', x2', x3', ...xn') then the correct average is =   A + [( x1+x2+ x3 +...xn) - (x1'+ x2'+ x3' + ...xn')]/n

33). Average of a series having common difference 2 is = first term + last term /2

34). If the average of n consecutive odd numbers is x , then the difference between the largest and smallest number is = 2(n-1)


35). If P distance is travelled by x km/h, Q distance with y km/h, R distance with z km/h, then average speed for whole journey is = (P+Q+R)/(P/x + Q/y + R/z) km/h

36). The average weight of group of X members is y, if after entering or exiting of a member , average weight become z, then weight of entering or exiting person is =
                                                                  z+-x(z-y)

37). The average weight of group of x person is y, when z person get enter/exit in the group , the average of group become w, then average of new entering/exiting persons is =  y +-(x/z +1)w

38). In the group of x persons , if a t years old person is replaced by a new person , then average is increased/ decreased by t1 , then age of new person is = t+-xt1

39). The average of n multiple of any number is = no.(n+1)/2

These are all the important arithmetic formulae on AVERAGE...

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Boat and stream short-tricks in Hindi | Fast track arithmetic formulae for competitive examination.

BOAT AND STREAM (नाव एवं धारा)
1). यदि शांत जल में नाव या तैराक की चाल x किमी/घंटा व धारा की चाल y किमी/घंटा है, तो धारा के अनुकूल नाव अथवा तैराक की चाल = (x+y) किमी/घंटा
2). धारा के प्रतिकूल नाव अथवा तैराक की चाल = (x-y) किमी /घंटा
3). नाव की चाल = (अनुप्रवाह चाल + उद्धर्वप्रवाह चाल)/2
4). धारा की चाल =  (अनुप्रवाह चाल - उद्धर्वप्रवाह चाल)/2
5). यदि धारा की चाल a किमी/घंटा है, तथा किसी नाव अथवा तैराक को उद्धर्वप्रवाह जाने में अनुप्रवाह जाने के समय का n गुना समय लगता है,(समान दूरी के लिए), तो शांत जल में नाव की चाल = a(n+1)/(n-1) किमी/घंटा
6). शांत जल में किसी नाव की चाल x किमी/घंटा व धारा की चाल y किमी/घंटा है, यदि नाव द्वारा एक स्थान से दूसरे स्थान तक आने व जाने में T समय लगता है, तो दोनो स्थानों के बीच की दूरी = T(x^2 - y^2)/2x km
7). कोई नाव अनुप्रवाह में कोई दूरी a घंटे में तय करती है, तथा वापस आने में b घंटे लेती है, यदि नाव कि चाल c किमी/घंटा है, तो शांत जल में नाव की चाल = c(a+b)/(b-a) km/h
8). यदि शांत जल में नाव की चाल a किमी/घंटा है, तथा वह b किमी/घंटा की चाल से बहती हुई नदी में गत…

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Dynamically changing India during early eighteenth century had a substantially growing economy under the authority of Mughal emperor Aurangzeb. But after his demise in 1707, several Mughal governors established their control over many regional kingdoms by exerting their authority. By the second half of eighteen century, British East India Company emerged as a political power in India after deposing regional powers and dominating over Mughal rulers. The present article attempts to analyze the reasons for emergence of British East India Company as an imperial political power in India and their diplomatic policies of territorial expansion. In addition to this, I briefly highlighted the Charter Acts (1773, 1793, 1813, 1833 and 1853) to trace its impact on the working process of Company.Establishment of East India Company in India

In 1600, British East India Company received royal charter or exclusive license…

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Three dimensional geometry (part-1) | study material for IIT JEE | concept booster , chapter highlights.

THREE DIMENSIONAL GEOMETRY

ORIGIN
In the following diagram X'OX , Y'OY and Z'OZ are three mutually perpendicular lines , which intersect at point O. Then the point O is called origin.
COORDINATE AXES 
In the above diagram X'OX is called the X axes, Y'OY is called the Y axes and Z'OZ is called the Z axes.
COORDINATE PLANES 
1). XOY is called the XY plane. 2). YOZ is called the YZ plane. 3). ZOX is called the ZX plane.
If all these three are taken together then it is called the coordinate planes. These coordinates planes divides the space into 8 parts and these parts are called octants.
COORDINATES  Let's take a any point P in the space. Draw PL , PM and PN perpendicularly to the XY, YZ and ZX planes, then
1). LP is called the X - coordinate of point P. 2). MP is called the Y - coordinate of point P. 3). NP is called the Z - coordinate of the point P.
When these three coordinates are taken together, then it is called coordinates of the point P.
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Speed , Distance and Time problems tricks in Hindi | fast track arithmetic formulae for problem solving.

SPEED , DISTANCE AND TIME PROBLEMS TRICKS IN HINDI
1). दूरी = चाल × समय
2). समय = दूरी/चाल
3). चाल = दूरी/समय
4). किलोमीटर को मील बनाने के लिए गुना किया जाता है =       5/8 से
5). मील को किलोमीटर बनाने के लिए गुना किया जाता है =       8/5 से
6). फुट - सेकंड को मील - घंटा बनाने के लिए गुना किया जाता है = 15/22 से
7). मील - घंटा को फुट - सेकंड बनाने के लिए गुना किया जाता है = 22/15 से
8). मी - सेकंड को किमी - घंटा बनाने के लिए गुना किया जाता है = 18/5 से
9). किमी - घंटा को मी - सेकंड बनाने के लिए गुना किया जाता है = 5/18 से
10). यदि एक व्यक्ति दो निश्चित स्थानों के बीच की दूरी a किमी/घंटा की चाल से खत्म करता है, तो t1 घंटे देर से पहुंचता है, तथा जब b किमी/घंटा की चाल से तय करता है, तब वह t2 घण्टे पहले पहुंचता है, तो दोनो स्थानों के बीच की दूरी =     ab(t1+t2)/(b-a) km
11). यदि कोई व्यक्ति a km/h की चाल से चलता है, तो वह अपनी मंजिल पर t1 घंटे लेट पहुंचता है, अगली बार वह अपनी चाल में b km/h की वृद्धि करता है, तो वह t2 घंटे लेट पहुंचता है, तब उसके द्वारा तय की गई दूरी = a(a+b)(t1-t2)/b
12). दो व्यक्ति X …