Quantitative Aptitude Formulas & Shortcut Tricks for All govt Jobs Exam

Quantitative Aptitude Formulas & Shortcut Tricks free download pdf percentages, Ratio/Proportion, Ages, Averages, Simple Compound Interest for Govt. Exams.

Quantitative Aptitude Formulas & Shortcut Tricks for All Govt Jobs Exam

Every year, the Indian government recruits employees in different corporations and departments across the country. Most exams require candidates to appear for an aptitude test or test, even if some recruit based solely on exam scores. Each of them has a quantitative aptitude section that mostly consists of mathematical sums. Practising formulas, tricks, and tips will help you earn top marks in this section. Here are topic-wise formulas for the quantitative aptitude section:

Following is the list of topics under quantitative aptitude.

List of topics:

Algebra
Alligations and mixtures
Area
Averages, Mean, Median and Mode
Boat Problems
Chain rule
Discount
Games and Races
Heights and distances
Inequalities
LCM and HCF
Linear Equations
Logarithms
Number theory
Number System – Fractions, Decimals
Partnerships
Percentage
Permutation and Combinations
Pipes and Cisterns
Points, lines and angles
Probability
Profit and Loss
Progressions
Quadratic Equations
Ratio and Proportions
Remainder theorem and unit digit
Sets and Venn Diagrams
Simple and Compound Interest
Simplification
Speed, Distance and Time
Stocks and shares
Surds, Indices, Exponents, and Powers
Surface area
Time and Work
Trains
Trigonometry
Volumes
Work and Wages

To solve quantitative aptitude questions, follow these steps:

The information should be read and understood carefully.
Analyze the important information.
The concept or formula should be applied to the situation.
Using the appropriate units, evaluate the answer.
Select the correct answer after verifying your calculations.

Tips and Formulas for Quantitative Aptitude

Percentage

Percent is derived from a phrase in latin “per centum” which means per hundred. It is a ratio with base (denominator) 100. It evolved as a concept so that there can be a uniform platform for comparing different values.

To express x% as a fraction, divide it by 100 ⇒ x% = x/100

To express a fraction as %, multiply it by 100 ⇒ x/y = [(x/y) × 100] %

x% of y is given by (y × x/100 )

Point to remember for faster Calculation

1/12 = 8.33%

1/11 = 9.09%

1/10 = 10%

1/9 = 11.11%

1/8 = 12.5%

1/7 = 14.28%

1 /6= 16.66%

1/5 = 20%

1/4 = 25%

1 /3= 33.33%

1 /2= 50%

1 = 100%

Shortcuts

If X’s income is a% more than Y’s income, the Y’s income is less than X’s income by

[ a / (100+a)] * 100%

If ‘M’ is x% of ‘N’ and ‘P’ is y% of ‘N’ then

‘M’ is (x/y) * 100% of ‘P’.

If the sides of the triangle, rectangle, square, circle, rhombus etc is

(i) Increased by a%. Its area is increased by

2a+(a2/100)

(ii)If decreased b%. Its areas is decreased by,

-2b+(b2/100)

The population of a town is ‘P’. It increased by x% during 1st year, increased by y% during 2nd year and again increased by z% during 3rd year. The population after 3 years will be,

P *[(100+x)/100] * [(100+y)/100] * [(100+z)/100]

Click Here To View Square Root Using Vedic Mathematics

SIMPLE AND COMPOUND INTEREST

Principal: – The money borrowed or lent out for certain period is called the principal or the Sum.

Interest: – Extra money paid for using other money is called interest

The cost of borrowing money is defined as Simple Interest. It is of two types – simple interest or compound interest. Simple interest(SI) is calculated only on the principal (P) whereas Compound interest(CI) is calculated on the principal and also on the accumulated interest of previous periods i.e. “interest on interest.” This compounding effect makes a big difference in the amount of interest payable on the principal.

Simple interest is:

Simple Interest = Principal x Interest Rate x Term of the loan(Time of Loan)

SI = P x i x n/100 when interest rate is taken in percent.

Compound Interest

CI = P [(1 + i)n – 1]

where P = Principal, i = annual interest rate in percentage terms, and n = number of compounding periods.

Number of compounding periods: When calculating compound interest, the number of compounding periods makes a significant difference. Compound interest is calculated on the basis that the higher the number of compounding periods, the greater the amount. Over a certain period of time, for every INR 100 principal, the amount of interest accrued at 10% annually will be lower than interest accrued at 5% semi-annually, which in turn will be lower than interest accrued at 2.5% quarterly.

The variables "i" and "n" in the compound interest formula must be adjusted if the number of compounding periods is more than once a year. This means that "i" has to be divided by the number of compounding periods per year, and "n" has to be multiplied by the number of compounding periods. As a result, for a 10-year loan with 10% interest compounded semiannually (number of compounding periods = 2), i = 5% (i.e. 10% / 2), and n = 20 (i.e. 10 x 2).

The table below shows how the number of compounding periods can affect the value of a INR 10,000 loan over time.

Shortcut Trick: Rule of 72

(72 / i) calculates the approximate time over which an investment will double at a given rate of return or interest. It is only applicable to annual compounding.

In 12 years, a 6% annual return investment doubles in value.

The return on an investment with a 9% rate of return will double after eight years.

PROFIT & LOSS

Cost Price-The price at which an article is purchased is known as cost price (C.P.)

Selling Price-The price at which the article is sold is known as selling price (S.P.)

These questions deals with Selling Price(P), And Cost price(CP). When selling price is greater than cost price then profit And when cost price is greater than selling price then loss.

Profit = SP-CP (SP>CP)

Loss = CP-SP (CP>SP)

It is very easy to answer questions about profit and loss. When solving profit loss questions in bank exams, keep in mind the following formulae.

Profit % = (Profit x 100)/CP

CP= {100 /(100+profit%)} x SP

CP={100/(100-loss%)} x SP

If there is a Profit of x% and loss of y % in a transaction, then the resultant profit or loss% is given by

[x – y – (x × y/100)]

Note- For profit use sign + in previous formula and for loss use – sign.

if resultant is positive then overall its profit. However, if it is negative then overall we have a loss.

If a cost price of m articles is equal to the selling Price of n articles,

(C.P of m article = S.P. of n article) then Profit percentage

(m – n)/n×100%

If m parts are sold at x% profit , n parts are sold at y % profit and p parts are sold at z% profit Rs. ‘R’ are earned as overall profit then the value of total consignment

R ×100 / (mx +ny +pz)

The same no. of article is purchased at a price of m rupee and the same at a price of n rupee. His gain or loss will depend on whether he sells them together at p a rupee

[{2mn/(m+n)p} -1]× 100

Marked price = Cost price + Markup

Always Remember: Markup is extra price on Cost Price. So, Markup is always calculated on CP

And

%Markup = [Markup/CP]*100

Discount (if SP < MP) = MP – SP i.e. SP = MP – Discount

Always remember: Discounts are deducted from the marked price. MP is always deducted from the discount.

%Discount = [Discount/MP]*100

AVERAGES

If there are N numbers, then their average is their sum divided by that, which is,

Average=(sum / N)

In a weighed average, the average of two sets of numbers is closer to the set with more numbers.

if 3 batsmen scored 25 runs and 2 batsmen scored 35 runs the average of the team won’t be 30. Rather it will be

= (25×3 + 35×2 )/5 = 29 . This is nearer to 25 since more batsmen scored 25 runs.

Average =total of data/No. of data

If the value of each item increases by x, then the average for the group will also rise by x.

If the value of each item is decreased by y, then the average of the group of items will also decrease by y.

If the value of each item is multiplied by the same value m, then the average of the group or items will also get multiplied by m.

If the value of each item is multiplied by the same value n, then the average of the group or items will also get divided by n.

The average of the combined group of items cannot be found based only on the average of the two groups individually.

Average of x natural no’s = (x+1)/2

Average of even No’s = (x+1)

Average of odd No’s = x

Change in the value of a Quantity and its effect on the Average

When one or more quantities are removed and replaced by the same number but with a different value,

Change in the no. of quantities and its effect on Average

+ = if quantities are Added, – = if quantities are removed

RATIO AND PROPORTION

Ratio is a fraction of two values. It can be represented in any of the following ways:

=> x/y, x : y , x÷y

In ratio of the form x : y, x is called as the antecedent/first term and y is the consequent/second term.

Generally, ratio is a handy way to compare two terms.

For example : 4 / π > 1 , it is clear that 4 > π

Comparing two numbers in a ratio requires that they be expressed in the same units. When x is expressed in meters and y in litres, they cannot be compared by using ratios, since they are expressed in different units.

Proportions are equal ratios/fractions.

If x : y = a : b, it can be written as x : y :: a : b and it is said that x, y, a, b are in proportion.

Here x and b are called extremes, while y and a are called mean terms.

Product of means=Product of extremes

Thus,

x :y :: a : b => (y∗a)=(x∗b)

If x : y=a : b

b is called the fourth proportional to x, y and a.

a is called the third proportional to x and y.

Sub-duplicate: Sub-duplicate ratio of (a:b) is (a^1/2: b^1/2)

Duplicate ratio of (a:b) is (a^2:b^2)

Triplicate Ratio:Triplicate ratio of (a:b) is (a^3:b^3)

Sub-triplicate Ratio: Sub-triplicate ratio of (a:b) is (a^1/3:b^1/3)

If a/b=c/d then, a+b/a−b=c+d/c−d This is known as Componendo and Dividendo.

We say that x is directly proportional to y, if x=ky for some constant k and we write, x∝y

We say that x is inversely proportional to y, if xy=k for some constant k and we write, x∝1y

Ages

Problems on Ages are asked in majority of bank and competitive examinations.

When you have practiced and know the formulae, they are generally easy to attempt. A few examples are:

If the current age isx, thenn times the age is nx.

If the current age isx, then agen years later/hence = x + n.

If the current age isx, then agen years ago = x – n.

The ages in a ratioa: b will be ax and bx.

If current age is x, then 1/n of the age is x/n.

Download free Quantitative Aptitude Formulae & Shortcut Tricks pdf for percentages, ratios/proportions, ages, averages, compound interest for government. For exams. Comment below with topics for more pdfs like these.