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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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