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Page 1
Quantitative Aptitude
Formula Book
Page 2
Quantitative Aptitude
Formula Book
Highlighted formulas are the shortcuts to get answer quickly.
1 2
Ber
Profit & loss
This is very commonly used section by most of
formulas & the companies. Here are important
definitions for you.
Cost price: T he price at which article is purchased
is known as C.P.
Selling price: T he price at which article is sold is
known as S.P.
Profit or gain: In mathematical terms we say if
S.P is greater than C.P , the n seller i s said to have
incurred profit or gain .
Loss: If Selling Price S.P is less than Cost price C.P ,
the seller is said to have incur red Loss.
Formulas to remember
?
Gain= (S.P) - ( C.P ) .
?
Loss= (C.P ) - ( S.P ).
?
L oss or gain is always reckoned on
C.P
?
Gain %= { gain*100}/ C.P .
?
Loss% ={loss*100}/C.P .
?
I f the article is sold at a gain of say
35 %, Then sp =135% of cp
?
I f a article is sold at a loss of say
35 %. Then Sp=65% of cp.
?
I f the trader professes to sell his
goods at Cp but uses false weights,
then Gain=[error/(true value)
( error)*100]%
Tricky formulas
?
S.P={(100+gain%) /100}*C.P.
?
S.P= {(100 - loss% )/100}*C.P.
?
C.P= {100/(100+gain%)} *S.P
?
C.P=100/(100 - loss%)}*S.P
?
When a person sells two items, one at a gain of x% and other at a loss of x%. Then the Seller
always incurs a loss given by : (x ² / 10)
?
If price i s first increase by X% and then decreased by Y% , the final change % in the price is
X - Y - XY/100
?
?
If price of a commodity is decreased by a % then by what % consumption should be increased to
keep the same price
(100*a) / (100 - 60)
Page 3
Quantitative Aptitude
Formula Book
Highlighted formulas are the shortcuts to get answer quickly.
1 2
Ber
Profit & loss
This is very commonly used section by most of
formulas & the companies. Here are important
definitions for you.
Cost price: T he price at which article is purchased
is known as C.P.
Selling price: T he price at which article is sold is
known as S.P.
Profit or gain: In mathematical terms we say if
S.P is greater than C.P , the n seller i s said to have
incurred profit or gain .
Loss: If Selling Price S.P is less than Cost price C.P ,
the seller is said to have incur red Loss.
Formulas to remember
?
Gain= (S.P) - ( C.P ) .
?
Loss= (C.P ) - ( S.P ).
?
L oss or gain is always reckoned on
C.P
?
Gain %= { gain*100}/ C.P .
?
Loss% ={loss*100}/C.P .
?
I f the article is sold at a gain of say
35 %, Then sp =135% of cp
?
I f a article is sold at a loss of say
35 %. Then Sp=65% of cp.
?
I f the trader professes to sell his
goods at Cp but uses false weights,
then Gain=[error/(true value)
( error)*100]%
Tricky formulas
?
S.P={(100+gain%) /100}*C.P.
?
S.P= {(100 - loss% )/100}*C.P.
?
C.P= {100/(100+gain%)} *S.P
?
C.P=100/(100 - loss%)}*S.P
?
When a person sells two items, one at a gain of x% and other at a loss of x%. Then the Seller
always incurs a loss given by : (x ² / 10)
?
If price i s first increase by X% and then decreased by Y% , the final change % in the price is
X - Y - XY/100
?
?
If price of a commodity is decreased by a % then by what % consumption should be increased to
keep the same price
(100*a) / (100 - 60)
Practice Examples
Example 1: The price of T.V set is increased by 40 % of the cost price and then decreased by 25% of
the new price. On selling, the profit for the dealer was Rs.1,000 . At what price was the T.V sold.
From the above mentioned formula you get:
Solution: Final difference % = 40-25-(40*25/100)= 5 %.
So if 5 % = 1,000 then 100 % = 20,000.
C.P = 20,000
S.P = 20,000+ 1000= 21,000.
Example 2: The price of T.V set is increased by 25 % of cost price and then decreased by 40% of the
new price. On selling, the loss for the dealer was Rs.5,000 . At what price was the T.V sold. From the
above mentioned formula you get :
Solution: Final difference % = 25-40-(25*45/100)= -25 %.
So if 25 % = 5,000 then 100 % = 20,000.
C.P = 20,000
S.P = 20,000 - 5,000= 15,000.
Example 3: Price of a commodity is increased by 60 %. By how much % should the consumption be
reduced so that the expense remains the same?
Solution: (100* 60) / (100+60) = 37.5 %
Example 4: Price of a commodity is decreased by 60 %. By how much % can the consumption be
increased so that the expense remains the same?
Solution: (100* 60) / (100-60) = 150 %
Page 4
Quantitative Aptitude
Formula Book
Highlighted formulas are the shortcuts to get answer quickly.
1 2
Ber
Profit & loss
This is very commonly used section by most of
formulas & the companies. Here are important
definitions for you.
Cost price: T he price at which article is purchased
is known as C.P.
Selling price: T he price at which article is sold is
known as S.P.
Profit or gain: In mathematical terms we say if
S.P is greater than C.P , the n seller i s said to have
incurred profit or gain .
Loss: If Selling Price S.P is less than Cost price C.P ,
the seller is said to have incur red Loss.
Formulas to remember
?
Gain= (S.P) - ( C.P ) .
?
Loss= (C.P ) - ( S.P ).
?
L oss or gain is always reckoned on
C.P
?
Gain %= { gain*100}/ C.P .
?
Loss% ={loss*100}/C.P .
?
I f the article is sold at a gain of say
35 %, Then sp =135% of cp
?
I f a article is sold at a loss of say
35 %. Then Sp=65% of cp.
?
I f the trader professes to sell his
goods at Cp but uses false weights,
then Gain=[error/(true value)
( error)*100]%
Tricky formulas
?
S.P={(100+gain%) /100}*C.P.
?
S.P= {(100 - loss% )/100}*C.P.
?
C.P= {100/(100+gain%)} *S.P
?
C.P=100/(100 - loss%)}*S.P
?
When a person sells two items, one at a gain of x% and other at a loss of x%. Then the Seller
always incurs a loss given by : (x ² / 10)
?
If price i s first increase by X% and then decreased by Y% , the final change % in the price is
X - Y - XY/100
?
?
If price of a commodity is decreased by a % then by what % consumption should be increased to
keep the same price
(100*a) / (100 - 60)
Practice Examples
Example 1: The price of T.V set is increased by 40 % of the cost price and then decreased by 25% of
the new price. On selling, the profit for the dealer was Rs.1,000 . At what price was the T.V sold.
From the above mentioned formula you get:
Solution: Final difference % = 40-25-(40*25/100)= 5 %.
So if 5 % = 1,000 then 100 % = 20,000.
C.P = 20,000
S.P = 20,000+ 1000= 21,000.
Example 2: The price of T.V set is increased by 25 % of cost price and then decreased by 40% of the
new price. On selling, the loss for the dealer was Rs.5,000 . At what price was the T.V sold. From the
above mentioned formula you get :
Solution: Final difference % = 25-40-(25*45/100)= -25 %.
So if 25 % = 5,000 then 100 % = 20,000.
C.P = 20,000
S.P = 20,000 - 5,000= 15,000.
Example 3: Price of a commodity is increased by 60 %. By how much % should the consumption be
reduced so that the expense remains the same?
Solution: (100* 60) / (100+60) = 37.5 %
Example 4: Price of a commodity is decreased by 60 %. By how much % can the consumption be
increased so that the expense remains the same?
Solution: (100* 60) / (100-60) = 150 %
Progressions
A lot of practice especially in this particular section will expose you to number of patterns. You need to
train yourself so that you can guess the correct patterns in exam quickly.
Formulas you should remember
Arithmetic Progression - An Arithmetic Progression ( AP) or a n arithmetic sequence is a series in
which the successive terms have a common difference. The terms of an AP either increase or
decrease progressively. For example,
1 , 3, 5,7, 9, 11,....
, 21, 14.5 , 34, 40.5 ..... . 27.5
?
Let the first term of the AP be a, the number of terms of the AP be n and the common
difference, that is the difference between any two successive terms be d.
?
The nth term, tn is given by:
?
The sum of n terms of an AP, Sn is giv en by the formulas:
o
or
?
( Where l is the last term (nth term in this case) of the AP ).
Geometric Progression -
A geometric progression is a sequence of numbers where each term
after the first is found by multiplying the previous term by a fixed number called the common
ratio.
Example: 1,3,9,27... Common ratio is 3.
Also a, b, c, d, ... are said to be in Geometric Progression ( GP) if b/a = c/b = d/c etc.
?
A GP is of the form etc. Where a is the first term and
r is the common ratio.
?
The n th term of a Geometric Progression is given by .
Page 5
Quantitative Aptitude
Formula Book
Highlighted formulas are the shortcuts to get answer quickly.
1 2
Ber
Profit & loss
This is very commonly used section by most of
formulas & the companies. Here are important
definitions for you.
Cost price: T he price at which article is purchased
is known as C.P.
Selling price: T he price at which article is sold is
known as S.P.
Profit or gain: In mathematical terms we say if
S.P is greater than C.P , the n seller i s said to have
incurred profit or gain .
Loss: If Selling Price S.P is less than Cost price C.P ,
the seller is said to have incur red Loss.
Formulas to remember
?
Gain= (S.P) - ( C.P ) .
?
Loss= (C.P ) - ( S.P ).
?
L oss or gain is always reckoned on
C.P
?
Gain %= { gain*100}/ C.P .
?
Loss% ={loss*100}/C.P .
?
I f the article is sold at a gain of say
35 %, Then sp =135% of cp
?
I f a article is sold at a loss of say
35 %. Then Sp=65% of cp.
?
I f the trader professes to sell his
goods at Cp but uses false weights,
then Gain=[error/(true value)
( error)*100]%
Tricky formulas
?
S.P={(100+gain%) /100}*C.P.
?
S.P= {(100 - loss% )/100}*C.P.
?
C.P= {100/(100+gain%)} *S.P
?
C.P=100/(100 - loss%)}*S.P
?
When a person sells two items, one at a gain of x% and other at a loss of x%. Then the Seller
always incurs a loss given by : (x ² / 10)
?
If price i s first increase by X% and then decreased by Y% , the final change % in the price is
X - Y - XY/100
?
?
If price of a commodity is decreased by a % then by what % consumption should be increased to
keep the same price
(100*a) / (100 - 60)
Practice Examples
Example 1: The price of T.V set is increased by 40 % of the cost price and then decreased by 25% of
the new price. On selling, the profit for the dealer was Rs.1,000 . At what price was the T.V sold.
From the above mentioned formula you get:
Solution: Final difference % = 40-25-(40*25/100)= 5 %.
So if 5 % = 1,000 then 100 % = 20,000.
C.P = 20,000
S.P = 20,000+ 1000= 21,000.
Example 2: The price of T.V set is increased by 25 % of cost price and then decreased by 40% of the
new price. On selling, the loss for the dealer was Rs.5,000 . At what price was the T.V sold. From the
above mentioned formula you get :
Solution: Final difference % = 25-40-(25*45/100)= -25 %.
So if 25 % = 5,000 then 100 % = 20,000.
C.P = 20,000
S.P = 20,000 - 5,000= 15,000.
Example 3: Price of a commodity is increased by 60 %. By how much % should the consumption be
reduced so that the expense remains the same?
Solution: (100* 60) / (100+60) = 37.5 %
Example 4: Price of a commodity is decreased by 60 %. By how much % can the consumption be
increased so that the expense remains the same?
Solution: (100* 60) / (100-60) = 150 %
Progressions
A lot of practice especially in this particular section will expose you to number of patterns. You need to
train yourself so that you can guess the correct patterns in exam quickly.
Formulas you should remember
Arithmetic Progression - An Arithmetic Progression ( AP) or a n arithmetic sequence is a series in
which the successive terms have a common difference. The terms of an AP either increase or
decrease progressively. For example,
1 , 3, 5,7, 9, 11,....
, 21, 14.5 , 34, 40.5 ..... . 27.5
?
Let the first term of the AP be a, the number of terms of the AP be n and the common
difference, that is the difference between any two successive terms be d.
?
The nth term, tn is given by:
?
The sum of n terms of an AP, Sn is giv en by the formulas:
o
or
?
( Where l is the last term (nth term in this case) of the AP ).
Geometric Progression -
A geometric progression is a sequence of numbers where each term
after the first is found by multiplying the previous term by a fixed number called the common
ratio.
Example: 1,3,9,27... Common ratio is 3.
Also a, b, c, d, ... are said to be in Geometric Progression ( GP) if b/a = c/b = d/c etc.
?
A GP is of the form etc. Where a is the first term and
r is the common ratio.
?
The n th term of a Geometric Progression is given by .
?
The sum of the first n terms of a Geometric Progression is given by
o
When r<1 2 .When r>1
?
When r =1 the progression is constant of the for a,a,a,a,a,...etc.
?
Sum of the infinite series of a Geometric Progression when |r|<1 is:
?
Geometric Mean (GM) of two numb ers a and b is given by
Harmonic Progression -
A Harmonic Progression ( ) HP is a series of terms where the reciprocals of
the terms are in Arithmetic Progression (AP).
?
The general form of an HP is /a, 1/(a+d), 1/(a+2d)>, 1/(a+3d), ..... 1
?
The n th the term Harmonic Progression tn=1/(nth is given by a term of of
corresponding arithmetic progression)
?
In the following Harmonic Progression: :
?
The Harmonic Mean (HM) of two numbers a and b is
?
The Harmonic Mean of n non - zero numbers is:
Few tricks to solve series questions
Despite the fact that it is extremely difficult to lay down all possible combinations of series, still if
you follow few steps, you may solve a series question easily & quickly.
Step 1: Do a preliminary screening of the series. If it is a simple series, you will be able to solve this
easily.
Step 2: If you fail in preliminary screening then determine the trend of the series. Determine
whether this is increasing or dec reasing or alternating.
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FAQs on Important Formulas of General Aptitude for GATE Exam - General Aptitude for GATE - Mechanical Engineering
| 1. What are some important formulas to remember for the General Aptitude section of the GATE Exam? |  |
Ans. Some important formulas to remember for the General Aptitude section of the GATE Exam include percentages, profit and loss, time and distance, time and work, averages, permutations and combinations, probability, etc.
| 2. How can I effectively prepare for the General Aptitude section of the GATE Exam? | |
Ans. To effectively prepare for the General Aptitude section of the GATE Exam, it is essential to practice regularly, solve previous year question papers, focus on understanding concepts rather than rote learning, and work on improving time management skills.
| 3. What types of questions can I expect in the General Aptitude section of the GATE Exam? | |
Ans. In the General Aptitude section of the GATE Exam, you can expect questions based on quantitative aptitude, reasoning ability, and verbal ability. These questions may test your numerical ability, logical reasoning, data interpretation, and language skills.
| 4. How can I improve my speed and accuracy in solving General Aptitude questions for the GATE Exam? | |
Ans. To improve speed and accuracy in solving General Aptitude questions for the GATE Exam, it is important to practice regularly, focus on building strong fundamentals, use shortcuts and tricks for calculations, and work on enhancing problem-solving skills.
| 5. Are there any specific topics within the General Aptitude section of the GATE Exam that are more important than others? | |
Ans. While all topics within the General Aptitude section of the GATE Exam are important, topics such as percentages, profit and loss, time and distance, time and work, and data interpretation are commonly tested and should be given special attention during preparation.
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