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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).…

NUMBER SYSTEM Shortcut and tricks for all competitive examination.

Today we are going to talk about some important arithmetic formulae on the chapter "number system". Which are very useful to all types of competitive examination. Readers are advised to learn all the formulae and keep practicing with it.

SOME IMPORTANT SUTRAS

1). Dividend = (divisor × quotient) + remainder
2). Quotient = (dividend - remainder)/divisor
3). Divisor = (dividend - remainder)/quotient
4). Remainder = dividend -(divisor × quotient)
5). Sum of n consecutive natural number=          n(n+1)/2

6). Sum of squares of n even numbers =    [n(n+1)/2]^2

7). Sum of multiples of x till to n = x.n(n+1)/2

8). Sum of squares of n odd numbers= 
                                                          n(2n-1)(2n+1)/3
9). Sum of squares of consecutive natural numbers till n =  n(n+1)(2n+1)/6

10). Sum of cubes of consecutive natural numbers till n = [n(n+1)/2]^2

11). Sum of consecutive even numbers till n =        n(n+1)/4

12). Sum of consecutive n odd numbers = n^2

13). Sum of consecutive odd numbers till n = 
                                                               (n+1/2)^2
14). Sum of n consecutive even numbers= n(n+1)

15). If any number is multiplied by any other number x and in the obtained results , when x is added then it is divisible by any other number y, then the smallest divisible number = [x(y-1)+x]

16). If any number is multiplied by any other number x and in the obtained results , when x is substracted then it is divisible by any other number y, then the smallest divisible number = [x(y+1)-x]

17). If x is the sum of a number of two digit and the number obtained by interchanging their digit , then the sum of the digit is = x/11

18). If y is the difference of a number of two digit and the number obtained by interchanging their digit , then the difference of the digit is = y/9

19). m the sum of the digit of any two digit number, if their digit are interchanged then the number become smaller by n from the original number. Then the original number(x,y) is = 
    x = m -[1/2({9m-n}/9)] , y =1/2({9m-n}/9) 

*. If number become greater by n then the original number (x,y) =
           x = m -[1/2({9m+n}/9)] , y =1/2({9m+n}/9)                               
20). If the sum of two numbers is x and their differences is y then their products is=(x^2-y^2)/4

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21). If the sum of the number and its square is x then the number is = [√(1+4x) - 1]/2

22). If x% of a number is n , then y% or z% of that number is = (yzn/x)×100

23). If the ratio of sum and difference of two numbers is a:b , then the ratio of that two numbers = a+b/a-b

24). If the difference of the original number and and the number obtained by interchanging their digit is x ,  then the difference of digit is = x/9

25). If the ratio between the two digit number and the sum of their digit is a:b , if unit place digit is n more than the digit in that of tens place. Then the number is given by = (9a/11b-2a)n
 *. Unit place digit = (10b-a/11b-2a)n
 *. Tens place digit = (a-b/11b-2a)n

26). If f(x) = x^n +K , is divided by x-1 , then the remainder is =
 *. Remainder = K+1, if K<(x-1)
 *. Remainder = (1+ remainder obtained when K is divided by x-1) , if K>(x-1)

27). When a number is divided by x1 and x2 separately , it leaves remainder r1 and r2 respectively. If that number is multiplied by x1×x2, then the remainder is = (x1×r2 + r1)

28). The numbers of zeros at the end of the product is given by;
 *. Number of zeros = 2^m×5^n if m>n
 *. Number of zeros = m if m<n

29). When a number is multiplied by x , then it increased by y , then the number is = y/(x-1)

30). If N is a composite number and it can be expressed as N = a^p.b^q.c^r.... , where a , b and C is different prime numbers and p ,q and r is positive integers, then number of divisor are =  (p+1).(q+1).(r+1)...

31). If a number is divided by N1 then it leaves remainder R , if same number is divided by N2 , then the remainder is = R/N2 , 
[ Note: N1>N2 , and N1 is divisible by N2]

32). If the sum of two numbers is x and their differences is y , then the difference in their squares is = xy

33). The difference of the squares of two consecutive numbers X and Y is = X+ Y

34). If the sum two numbers is X and the sum of their squares is Y , then
 *. The product of the numbers = X^2-Y/2
 *. The numbers are = [X-√(2Y-X^2)]/2 and        [X +√(2Y-X^2)]/2

35). If the sum of the squares of two numbers is x and the squares of their differences is y , then the product of that two numbers is = (x-y)/2

36). If the product of two numbers is x and the sum of their squares is y , then the sum of the two numbers is √(y+2x) and the difference of two numbers is √(y-2x).

37). If the denominator of a rational number is d more than to its numerator. If numerator is increased by x , and denominator is decreased by y. Then we obtained P. Then the rational number is =
                                           [x-P(d-y)/x+(yP-d)]

38). When A is added to another number B then total (A+B) becomes p% of number B. Then the ratio between A and B is =
(p-100/100)

39). When the two different number is divided by the same divisor , they leave remainder x and y respectively. If their sum is divided by the same divisor then remainder is z , then the divisor is = (x+y-z)

40). If the product of two numbers is x and their sum is y , then the two numbers is = 
  [y+√(y^2-4x)]/2 and   [y-√(y^2-4x)]/2

41). If the product of two numbers is x and their differences is y , then the two numbers is = √(y^2+4x)+y/2 and  √(y^2+4x)-y/2

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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…

Emergence of British East India Company as an Imperialist Political Power in India

EMERGENCE OF BRITISH EAST INDIA COMPANY AS AN IMPERIALIST POLITICAL POWER IN INDIA
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…

CORONA VIRUS, history of origin , discovery , infection mechanism, symptoms and treatment.

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OVERVIEW OF CORONAVIRUS
According to the biological study , Coronavirus is a cluster of viruses that causes diseases in birds and mammals. Therefore humans are also mammals then in human being this viruses cause respiratory infections , and one of the respiratory infections is mild common cold. Coronavirus can lead to diarrhea in cows and pigs but in chicken they can cause upper respiratory infections. Currently there is no vaccine or antiviral drugs for the treatment of diseases caused by Coronavirus.
BIOLOGICAL INTRODUCTION OF coV
The family of Coronavirus is coronaviridae, and it's subfamily is Orthocoronavirinae and order is Nidovirales, Coronavirus is a member of Orthocoronavirinae subfamily. All Coronavirus is coated with positive sense single …

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.
SIGN CONVENTI…

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 …