100+ Aptitude Shortcuts for SSC CGL, CAT, MBA, CHSL, GMAT Exams

Quantitative Aptitude Short Cuts & Tricks for SSC CGL CHSL MTS BANK PO Staff Selection Commission, Combined Graduate Level Exam, Maths study material for Bank PO exams Question Bank from Previous Papers.

• Quadratic Equations–Important Formulas
• Cyclic Quadrilateral
• Train & Distance : 7 Important Shortcuts 
• Dates and Calendars - Zeller's Rule Shortcut
• Boats and Streams: 8 Important Shortcuts 
• Pipes and Cisterns: 5 Important Shortcuts 
• Time and Distance: 8 Shortcuts 
• Time and Work: 13 Important Shortcuts
• Profit and Loss: 14 Important Shortcuts 
• Simple Interest: 7 Important Shortcuts 
• Compound Interest: 10 Important Shortcuts 
• Clocks & Time: 8 Important Shortcuts 
• TYPES OF NUMBERS
• TESTS OF DIVISIBILITY OF NUMBERS
• H.C.F and L.C.M of Numbers

Dates and Calendars - Zeller's Rule Shortcut

Calculate the day of the week for any date. Zeller’s Rule can be used to find the day on any particular date in the calendar in the history. All you have to know is the formula given below and how to use it.

Zeller’s Rule Formula:

F = K + [(13xM - 1)/5] + D + [D/4] + [C/4] – 2C

where, K = Date, M = Month, C = The first two digits year and D = Last two digits of the year

* In Zellers rule, months start from March. March = 1, April = 2, May = 3 and so on… till Dec = 10,

Jan = 11 Feb. = 12

* Also remember that when you have to find day of the first or second month of any year, then Year=Given year-1 i.e., When you want to find Day of 15-2-1990., K=15, Month=12, D=Given Year-1=1990-1=1989=89

Ex: find the day of the 27-08-2014 ?

Boats and Streams: 8 Important Shortcuts & Tricks Explained with Examples

Stream: Moving water of the river is called stream.

Still Water: If the water is not moving then it is called still water.

Upstream: If a boat or a swimmer moves in the opposite direction of the stream then it is called upstream.

Downstream: If a boat or a swimmer moves in the same direction of the stream then it is called downstream.

Points to remember

i. When speed of boat or a swimmer is given then it normally means speed in still water.

ii. If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,

    Speed of boat or swimmer upstream = (x − y) km/h

     Speed of boat or swimmer downstream = (x + y) km/h

iii. Speed of boat or swimmer in still water is given by

= 1/2(Downstream + Upstream)

Speed of stream is given by

= 1/2(Downstream - Upstream)

Some Shortcut Methods

Train & Distance : 7 Important Shortcuts Explained

Concept: Problems on trains and ‘Time and Distance’ are almost same. The only difference is we have to consider the length of the train while solving problems on trains.

A train is said to have crossed an object (stationary or moving) only when the last coach (end) of the train crosses the said object completely. It implies that the total length of the train has crossed the total length of the object.

Hence, the distance covered by the train = length of train + length of object

Points To Remember

1. Time taken by a train of length of L meters to pass a stationary pole is equal to the time taken by train to cover L meters.

2. Time taken by a train of length of L meters to pass a stationary object of length P meters is equal to the time taken by train to cover (L + P) meters.

3. Relative speeds :

i. If two trains are moving in same direction and their speeds are x km/h and y km/h (x > y) then their relative speed is (x –y) km/h.

ii. If two trains are moving in opposite direction and their speeds are x km/h and y km/h then their relative speed is (x + y) km/h.

Unit Conversion:

i. To convert 'X' Km/hr into m/s

    -  Multiply X with 5/18

ii. To convert 'x' m/s into Km/hr

    -  Multiply x with 18/5

Some Shortcut Methods

Pipes and Cisterns: 5 Important Shortcuts with Solved Examples

Pipe and Cistern problems are similar to time and work problems. A pipe is used to fill or empty the tank or cistern.

Inlet Pipe: A pipe used to fill the tank or cistern is known as Inlet Pipe.

Outlet Pipe: A pipe used to empty the tank or cistern is known as Outlet Pipe.

Some Basic Formulas

1. If an inlet pipe can fill the tank in x hours, then the part filled in 1 hour = 1/x

2. If an outlet pipe can empty the tank in y hours, then the part of the tank emptied in 1 hour = 1/y

Some Shortcut Methods

Time and Distance: 8 Shortcuts & Tricks explained with solved examples

The terms time and distance are related to the speed of a moving object.

Speed: Speed is defined as the distance covered by an object in unit time.

   Speed = Distance/Time

Some Important Facts:

*  Distance travelled is proportional to the speed of the object if the time is kept constant.

*  Distance travelled is proportional to the time taken if speed of object is kept constant.

 *  Speed is inversely proportional to the time taken if the distance covered is kept constant.

*  If the ratio of two speeds for same distance is a:b then the ratio of time taken to cover the distance is b:a

Relative Speed:

 i.  If two objects are moving in same direction with speeds of x and y then their relative speed is (x - y)

ii.  If two objects are moving in opposite direction with speeds of x and y then their relative speed is (x + y)

Unit Conversion:

i. To convert 'X' Km/hr into m/s

    -  Multiply X with 5/18

ii. To convert 'x' m/s into Km/hr

    -  Multiply x with 18/5

Some Important Shortcut Formulas

Time and Work: 13 Important Shortcuts

Time and Work problems are most frequently asked problems in quantitative aptitude.Technically speaking, Work is the quantity of energy transferred from one system to another but for question based on this topic Work is defined as the amount of job assigned or the amount of job actually done.Problem on work are based on the application of concept of ratio of time and speed.Work is always considered as a whole or one.

There exists an analogy between the time speed and distance. To solve these problems very quickly, you should understand the concept of Time and Work and some shortcut methods.If a man can do a piece of work in 5 days, then he will finish 1/5th of the work in one day. If a man can finish 1/5th of the work in one day then he will take 5 days to complete the work. If a man 5/6th of work in one hour then he will take 6/5 hours to complete the full work. If A works three times faster than B then A takes 1/3rd the time taken by B.

Here are some shortcut rules which can be very useful while solving Time and Work problems.

Trick-1: M1 men can do a piece of  W1 work in D1 days. the number of days will required to complete the work by M2 men is given by (M1*D1)/W1 = (M2*D2)/W2

Ex: 15 men can do a piece of work in 50 days.how many days will required to complete the work by 10 men ?

a. 55      b. 65       c. 75       d. 70

Sol: M1=15, M2=10  &  D1=50, D2=?

       W1=W2=1

  So, D2=[15*50]/10=75 days

Profit and Loss: 14 Important Shortcuts & Tricks Explained

Profit and loss problems are frequently asked problems in competitive exams. Profit and loss is the branch of basic mathematics which deals with the study of profit and loss made in a business transaction. The profit and loss account is fundamentally a summary of the trading transactions of a business and shows whether it has made a profit or loss during a particular period of account. Indeed, by deducting the total expenditure from total income the profit or loss of a business can be calculated. Along with the balance sheet, it is one of the key financial statements that make up a company's statutory accounts. Basically, this type of account shows the following information for a business:

a) Sales revenue earned by business

b) Cost of sales that the business has incurred

c) Other operating costs incurred by the business

d) Profit/Loss earned by business.

Profit and loss is mainly used in finance and business transactions. Some important profit and loss formulas are: Notations used in profit and loss: S.P. – Selling price C.P. – Cost price M.P. – Marked Price.

Points to remember :

* To find profit or loss when cost price and selling price are given.

(i). When Selling Price > Cost Price, There is a Profit and it is given by Selling Price - Cost Price.

(ii). When Selling Price < Cost Price, There is a Loss and it is given by Cost Price - Selling Price.

* The Profit or Loss is generally reckoned as so much per cent on the cost.

  Gain or loss per cent

        = ( Loss or Gain / CP )× 100

*  C.P in terms of S.P and P%

        C.P = [ (S.P *100)/(100+P%) ]

*  C.P in terms of S.P and  L%

        C.P = [ (S.P *100)/(100-L%) ]

*  S.P in terms of C.P and P%

        S.P = [ C.P*(100+P%)/100 ]

*  S.P in terms of C.P and L%

        S.P = [ C.P*(100-L%)/100 ]

Simple Interest: 7 Important Shortcuts Explained

When a person borrows some money from another person then the borrower has to pay some extra money for the use of that money to the lender. This extra money is called Interest.In other words, the amount charged by lender for giving his money for a specific amount of time is called Interest.

The amount of money borrowed is known as Principle. Total of Interest and Principle is known as Total Amount.

Amount = Principle + Interest.

The borrower has to pay interest according to some percent of principle for the fixed period of time. This percentage is known as Interest Rate.This fixed period may be a year, six months, three months or a month and correspondingly the rate of interest is charged annually, half yearly, quarterly or monthly.

Some Basic Formulas

If A = Amount P = Principle

I = Interest T = Time in years

R = Interest Rate Per Year, then

* Amount = Principle + Interest

      A = P + I

*    I = ( P*T*R )/100

*    P= (I*100)/(T*R)

*    T= (I*100)/(P*R)

*    R= (I*100)/(P*T)

Trick-1: If a sum of money become “X” times in “T” years, at Simple Interest, then the rate of interest “R%” is given by:

Compound Interest: 10 Important Shortcuts & Tricks explained with Examples

Majority of business operations and goes by the name of Compound Interest. The basic concept operating behind compound interest is very simple. 

For example, Sham borrows a sum of Rs. 100 from Ghansham for a period of two years. The rate of interest for this loan is 10%. At the end of year one, the amount due is the principal and 10% interest on it, that is a total of Rs. 110. Now, effectively the principal value of the loan for the second year is no longer Rs. 100, it is in fact Rs. 110. That is what Ghansham would say and believe. According to him, for the 2nd year, he has lent Rs. 110 as that was the amount he would have had if he taken back the money at the end of year 1. Now for the 2nd year, the interest becomes Rs. 11 (10% of Rs. 110) and the total amount Ghansham would get would be Rs. 121.

If the same calculation was done using the logic of simple interest, you would see that the interest due for two years would be Rs. 20 (10% of Rs. 100 for two years). Thus, replace a S with a C and there is such a big difference in the calculations carried out.

Effectively, for compound interest, the 2nd term of interest is actually the sum total of the principal and the interest for the first term.

Compound Interest Tool tip 1: The Definitions

Principal (P): The original sum of money loaned/deposited. Also known as capital.

Interest (I): The amount of money that you pay to borrow money or the amount of money that you earn on a deposit.

Time (T): The duration for which the money is borrowed. The duration does not necessarily have to be years. The duration can be semi-annual, quarterly or any which way deemed fit.

Rate of Interest (R):  The percent of interest that you pay for money borrowed, or earn for money deposited.

Compound Interest Tool tip 2: The Basic Formula

Clocks & Time: 8 Important Shortcuts Explained

We need to get couple of basic facts clear:

* Speed of the hour hand = 0.5 degrees per minute (dpm) {The hour hand completes a full circle or 360 degrees in 12 hours or 720 minutes}

* Speed of the minute hand = 6 dpm {The minute hand completes a full circle in 60 minutes}

* At ‘n’ o’ clock, the angle of the hour hand from the vertical is 30n

Clock problems can be broadly classified in two categories:

a) Problems on angles

b) Problems on incorrect clocks

c) Problems on angles

Finding the angle between the hands category clock problems  major questions which is quite time taking and difficult to solve.

Some easy tricks to solve

TYPES OF NUMBERS

I. Natural Numbers : Counting numbers I, 2. 3, 4, 5, ..... are called natural artillery.

2. Whole Numbers : All counting numbers together with zero form the set of whole number. Thus,

   (A) 0 is the only whole number which is not a natural number.

   (B) Every natural number is a whole number

3. Integers : All natural numbers. 0 and negatives of counting numbers ie., - 3, - 2, - 1. 0. 

I. 2, 3...... together form the set of integers

(A) Positive Integers t 11. 2. 3, 4, .....I is the set of all positive integers.

(B) Negative Integers : (- I, - 2, - 3......I is the set of all negative integers.

(C) Non-Positive and Non-Negative integers : 0 is neither positive nor negative. 

    So, 0, 1, 2, 3. ..... I represents the set of non-negative integers, while (0, - I, - 2, - 3,  ) 

    represents the set of non-positive integers.

TESTS OF DIVISIBILITY OF NUMBERS (ShortCuts)

I. Divisibility By 2 : A number is divisible by 2. if its unit's digit is any of 0, 2. 4. 6. 8.Ex. 84032 is divisible by 2. while 05935 is not.

Consider a two digit number (10*a+b). Factor this to 2*5*a + b. This shows that all numbers ending a zero are divisible by two, so if the ones digit is divisible by two, the entire number is as well.

2. Divisibility By 3 : A number is divisible by 3, if the sum of its digits is divisible by 3.
Consider a 2 digit number 10*a + b = 9*a + (a+b). 
We know that 9*a is divisible by 3, so 10*a + b will be divisible by 3 if and only if a+b is. 
Similarly, 100*a + 10*b + c = 99*a + 9*b + (a + b + c), and 99*a + 9*b is divisible by 3, so the total will be divisible by 3 if and only if a + b + c is. 

Ex. 592482 is divisible by 3, since sum of its digits = (5 + 9 + 2 +4 + 8 + 2) = 30, which is divisible by 3. But, 804329 is not divisible by 3, since sum of its digits • (8 +0+ 4 + 3 + 2 + 9)= 32. which is not divisible by 3.

3. Divisibility By 4 : A number is divisible by 4, if the number formed by the last two digits is divisible by 4.
Consider a three digit number (100*a + 10*b + c)
Factor the first digit: 4*25*a + 10*b + c 

Ex. 892648 is divisible by 4, since the number formed by the last two digits is 48. which is divisible by 4. But, 749282 is not divisible by 4. since the number formed by the last two digits is 82, which is not divisible by 4.

H.C.F and L.C.M of Numbers (Shortcuts)

I. Factors and Multiples : If a number a divides another number b exactly, we say that a is a factor of b.  In this case, b is called a multiple of a

II. Highest Common Factor (H.C.F.) or Greatest Common Measure(G.C.M.) or Greatest Common Divisor (G.C.D.)  The H.CF of two or more than two numbers is the greatest number that divides each of them exactly.
There are two methods of finding tho H.C.F of a given set of numbers

1.    Factorization Method : EXpress each one of the given numbers as the product of prime factors
 The product of least powers of common prime factors gives H.C.F

2.    Division Method: Suppose we have to find the H.C.F of two given numbers. Divide the larger number  by the smaller one. Now divide the divisor by the remainder Ripeat the process of dividing the preceding number  by the remainder last obtained till zero is obtained as remainder. The lastt divisor is the required H.C.F. 
Finding the H.C.F. of more than two numbers : Suppose we have to find the H.C.F. of three numbers then H.C.F. of ( H.C.F of any two) and (the third number ) gives the H C F of three given numbers.  Similarly the H.C.F of more than three numbers may be obtained.