|Quantitative Aptitude Important Formulas Logical ReasoningGeneral Knowledge of MPGeneral Knowledge of India|
Problems On Trains - Important Formulas,Tricks and Examples
When a train of lengths L travelling at a speed S crosses a pole/pillar/flag post in time T, then the equation is given as S =L/T
When a train of lengths L1 travelling at a speed S1 crosses a platform/bridge/tunnel of length L2 in time T, then the equation is given as S1 = (L1+L2)/T
Relative speed when moving in opposite direction is S1 +S2
When two trains of lengths L1 and L2 respectively travelling at the speeds of S1 and D2 respectively cross each other in time T, then the equation is given as S1+S2 = (L1+L2)/T
When a train of lengths L1 travelling at a speed S1 overtakes another train of length L2 travelling at speed S2 in time T, then the equation is given as S1 - S2 = (L1+L2)/T
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Numbers - Important Formulas,Tricks and Examples
The common number system is decimal number system.
Types of Numbers
Natural Numbers:The numbers that are used for counting called Natural Numbers.These are infinite and start from the number 1 .
Whole numbers:The whole numbers are just all the natural numbers plus zero.
Integers: Integers incorporate all positive and negative numbers with zero.
Even Numbers: An even number is one that can be divided evenly by two leaving no remainder, such as 2, 4, 6, and 8.
Odd Numbers: An odd number is one that does not divide evenly by two, such as 1, 3, 5, and 7.
Rational Numbers: All numbers of the form p/q where p and q are integers (q ≠ 0) called Rational numbers.
Irrational Numbers: Irrational numbers are the opposite of rational numbers. An irrational number cannot be written as a fraction as p/q where a and b are integers.
Real numbers: Real numbers include counting numbers, whole numbers, integers, rational numbers and irrational numbers.
Prime Number: A prime number is a number which can be divided only by 1 and itself. The prime number has only two factors, 1 and itself.
Composite Number: A Composite Number is a number which can be divided evenly. Any composite number has additional factors than 1 and itself.
Co-primes or Relatively prime numbers: A pair of numbers not having any common factors other than 1 or –1. (Or alternatively their greatest common factor is 1 or –1)
Twin Primes: A pair of prime numbers is said to be twin primes if they differ by 2.
(a+b)2 = a2 + 2ab + b2
(a+b)2 - (a-b)2 = 4ab
a2-b2 = (a-b)(a+b)
(a+b)3 = a3+b3+3ab(a+b) = a3+b3+3a2b+3ab2
a3+b3 =(a+b)3-3ab(a+b) = (a+b)(a2-ab+b2)
Test of Divisibility
Divisibility By 2 : A number is divisible by 2, if its unit's digit is zero or even (2, 4, 6, 8..).
Divisibility By 3 : A number is divisible by 3, if the sum of its digits is divisible by 3.
Divisibility By 4 : A number is divisible by 4, if the number formed by the last two digits is divisible by 4.
Divisibility By 5 : A number is divisible by 5, if its unit's digit is either 0 or 5.
Divisibility By 6 : A number is divisible by 6, if it is divisible by both 2 and 3.
Divisibility By 8 : A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8.
Divisibility By 9 : A number is divisible by 9, if the sum of its digits is divisible
Divisibility By 10 : A number is divisible by 10, if it ends with 0.
Divisibility By 11 : A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11.
Divisibility By 12: A number is divisible By 12 if the number is divisible By both 4 and 3.
Divisibility By 13: A number is divisible By 13 if its unit’s place digit is multiplied By 4 and added to the remaining digits and the number obtained is divisible By 13.
Divisibility By 14: A number is divisible By 14 if the number is divisible By both 2 and 7.
Divisibility By 15: A number is divisible By 15 if the number is divisible By both 3 and 5.
Divisibility By 16: A number is divisible By 16 if its last 4 digits is divisible By 16 or if the last four digits are zeros.
Divisibility By 17: A number is divisible By 17 if its unit’s place digit is multiplied By 5 and subtracted from the remaining digits and the number obtained is divisible By 17.
Divisibility By 18: A number is divisible By 18 if the number is divisible By both 2 and 9.
Divisibility By 19: A number is divisible By 19 if its unit’s place digit is multiplied By 2 and added to the remaining digits and the number obtained is divisible By 19.
Divisibility By 20: A number is divisible by 20 if it is divisible by 10 and the tens digit is even.
|Ratio and Proportion|
A certain sum of money is divided between A and B in the ratio of 5/4 : 5/3 and A got Rs. 360/-. Find the total sum of money and B’s share?
In an office, the ratio of the salaries of an officer and a clerk is 15:7. If the salary of a clerk is Rs. 720/- less than the salary of the officer, find the salary of each?
In an election to a municipal council, the votes secured by two candidates are in the ratio 13:19. The elected candidates gets 312 votes more than the second candidate. How many votes are secured by the second candidate?
A certain sum of money is divided between Murthy and Prasad in the ratio 22/7 : 8/3. If Murthy gets Rs. 120/- more than Prasad, find the share of each?
In a cricket test series, the runs made by Raju and Tendulkar are in the ratio 5:9 and Tendulkar and Azar are in the ratio 6:7. What are the runs made by them if Azar makes 187 runs more than Raju?
If A:B = 2:3 and B:C = 9:5 find A:B:C?
If A:B = 3/5:5/7 and B:C = 3/4:2/5, find A:B:C?
If R:S = 0.01:0.11 and S:T = 2.2:1, Find R:S:T?
In a school, Under a Saving Scheme, Rekha saves 3/2 times the savings of Bindu, Geeta saves 4 times the savings of Rekha. Find the ratio of the savings of all the three in least terms?
A man left 1/3 rd of his property to his wife and 3/5 th of the remainder to his daughter. He gave the rest to his son who received Rs. 6400/-. How much was his original property worth?
|Ratio and Proportion|
In a school 4/9 of the pupils are boys. There are 125 girls. How many boys are there?
If A:B = 3:4 and B:C = 5:6, find A:C?
IF X:Y = 3:4 AND Y:Z = 4:5, FIND X:Y:Z?
A house site is in the shape of a square. Its area is 1225 sq metres. What is its perimeter?
The area of a square field is 7396 sq metres. Find its perimeter?
Twice the first of three consecutive even integer is 6 more than the second integer. What is the third integers?
|Ratio and Proportion|
If 2x=3y and 4y=5z, then what is x:z=?
What quantity must be added to each term of the ratio a + b : a – b to make it equal to (a + b)2 : (a – b)2 ?
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