R S Aggarwal Quantitative Aptitude Free PDF Download
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Basic maths formula
A formula is a mathematical expression or definite rule that is derived from the relation between two or more quantities and the derived final product is expressed in symbols. The formulas of mathematics included numbers known as constants, letters that represent the unknown values and are known as variables, mathematical symbols known as signs, and exponential powers in some cases.
Algebra
Algebra is an elementary subject of mathematics that deals with the study of the evaluation of numbers and symbols. The algebraic operations are carried out to determine the unknown values which are expressed by letters. Algebraic equations are the expressions formed by the combination of variables, constants, factors, and coefficients of variables.(R S Aggarwal Quantitative Aptitude Free PDF)
Basic algebra formula
a2 – b2 = (a – b)(a + b)
(a + b)2 = a2 + 2ab + b2
a2+ b2 = (a + b)2 – 2ab
(a – b)2 = a2 – 2ab + b2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
(a + b)3 = a3 + 3a2b + 3ab2 + b2
(a – b)3 = a3 – 3a2b + 3ab2 – b3
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
a4– b4 = (a – b)(a + b)(a2 + b2)
(am)(an) = am + n
(ab)m = ambm
(am)n = amn(R S Aggarwal Quantitative Aptitude Free PDF)
Arithmetic
Arithmetic is the oldest method of calculation known till now. The word arithmetic is derived from the Greek words ‘arithmos’ which literally means numbers. Brahmagupta the Indian mathematician is known as the ‘father of arithmetic‘. And, the Fundamental theory of number theory was proposed by Carl Friedrich Gauss in 1801.(R S Aggarwal Quantitative Aptitude Free PDF)
The basic operations involved in arithmetic are addition, subtraction, multiplication, and division.
Arithmetic formula
Arithmetic mean (average) = Sum of values/Number of values.
Geometry
Geometry is a part of mathematics that is concerned with the study of shapes, sizes, parameters, measurement, properties, and dimensions. There are generally three types of geometry. They are Euclidean geometry, Spherical geometry, and Hyperbolic geometry.(R S Aggarwal Quantitative Aptitude Free PDF)
Basic geometry formula
Rectangle
Perimeter of Rectangle = 2(l + b)
The area of Rectangle = l × b
Where ‘l’ is Length and ‘b’ is Breadth(R S Aggarwal Quantitative Aptitude Free PDF)
Square
The area of Square = a2
The perimeter of Square = 4a
Where ‘a’ is the length of the sides of a Square
Triangle
Area of Triangle= 1/2 × b × h
Where ‘b’ is the base of the triangle and ‘h’ is the height of the triangle
Cube
Surface Area of Cube = 6a2(R S Aggarwal Quantitative Aptitude Free PDF)
Where ‘a’ is the length of the sides of the Cube
Circle
Area of Circle = π × r2
Circumference of Circle = 2πr
Where ‘r’ is the radius of a Circle
Trapezoid
Area of Trapezoid = 1/2 × (b1 + b2) × h
Where b1 and b2 are the bases of the Trapezoid
And, h = height of the Trapezoid(R S Aggarwal Quantitative Aptitude Free PDF)
Cone
The curved surface area of a cone = πrl
Total surface area of cone = πr(r + l) = πr[r + √(h2 + r2)]
Volume of a Cone = V = 1/3× πr2h
Here, ‘r’ is the radius of the base of Cone and h = Height of the Cone
Sphere
Surface Area of a Sphere = S = 4πr2
Volume of a Sphere = V = 4/3 × πr3
Where, r = Radius of the Sphere(R S Aggarwal Quantitative Aptitude Free PDF)
Cylinder
The curved surface area of Cylinder = 2πrh
The total surface area of Cylinder = 2πr(r + h)
The volume of Cylinder = V = πr2h
Where ‘r’ is the radius of the base of the Cylinder
And, ‘h’ is the height of Cylinder
Probability
Probability is the mathematical term used to determine the chance of occurring a particular event. Probability can simply be defined as the possibility of the occurrence of an event. It is expressed on a linear scale from 0 to 1. There are three types of theoretical probability, experimental probability, and subjective probability.
Basic probability formula
P(A) = n(A)/n(S)
Where,
P(A) is the probability of an event.
n(A) is the number of favorable outcomes
n(S) is the total number of events(R S Aggarwal Quantitative Aptitude Free PDF)
Fraction
A fraction is a number expressed with integers in which a numerator is divided by the denominator. A fraction is basically the quotient of a division.
Basic fractions formula
(a + b/c) = (a × c) + b/c
(a/b + d/b) = (a + d)/b
(a/b + c/d) = (a × d + b × c/b × d)
a/b × c/d = ac/bd
(a/b)/(c/d) = a/b × d/c(R S Aggarwal Quantitative Aptitude Free PDF)
Percentage
A percentage is a numerical value or ratio expressed as a fraction of 100. It is generally symbolized by the sign %.
Basic percentage formula
Percentage = (Amount in the category/Total value) × 100
Sample problems
Question 1:
Punam has 4/5 parts of the field among which she uses 2/5 parts for farming. How much part of the farm is left for other purposes?(R S Aggarwal Quantitative Aptitude Free PDF)
Solution:
Given:
The total fraction of land 4/5.
The total fraction used for farming 2/5.
Now,
=> 4/5 – 2/5
=> 4 – 2/5
=> 2/5
Hence, 2/5 part of the field left.(R S Aggarwal Quantitative Aptitude Free PDF)
(R S Aggarwal Quantitative Aptitude Free PDF)
Question 2:
Simplify 3/(x – 1) + 1/(x(x – 1) = 2/x
Solution:
=> 3x + 1/x(x – 1) = 2(x – 1)/x(x – 1)
=> 3x + 1 = 2(x – 1)
=> x = -3
(R S Aggarwal Quantitative Aptitude Free PDF)
Question 3:
If x + 1/x = 3. Find the value of x2 + 1/x2.
Solution:
=> (x + 1/x)2 = (3)2
=> x2 + 2 × x × 1/x + (1/x)2 = 9
=> x2 + 1/x2 + 2 = 9
=> x2 + 1/x2 = 7(R S Aggarwal Quantitative Aptitude Free PDF)
Question 4:
If the radius of a circle is 21cm. Find the area of the given circle.
Solution:
Given:(R S Aggarwal Quantitative Aptitude Free PDF)
The radius of the circle is 21cm.
We have,
Area of the circle (A) = πr2
=> 22/7 × 21 × 21
=> 1386cm2
Hence, the area of the given circle is 1386cm2
(R S Aggarwal Quantitative Aptitude Free PDF)
Question 5:
Find the area of a triangle having a base of 100cm and a height of 20cm.
Solution:(R S Aggarwal Quantitative Aptitude Free PDF)
Given:
The base of the triangle is 100cm.
The height of the triangle is 20cm.
We have,
Area(A) = 1/2 × b × h
=> 1/2 × 10 × 20
=> 1000cm2
(R S Aggarwal Quantitative Aptitude Free PDF)
Question 6:
Determine the probability to get an ace from a card taken from a deck.(R S Aggarwal Quantitative Aptitude Free PDF)
Solution:
Given:
Total number of favorable outcomes n(S) = 52
Number of face cards in the deck = 12
Number of favorable outcomes n(A) = 12
Now,
P(A) = n(A)/n(S)
=> 12/52
=> 3/13
Hence, the probability to get a face card from a card deck is 3/13.(R S Aggarwal Quantitative Aptitude Free PDF)
Question 7:
What will be the 20% of 240kg?
Solution:
=> 20/100 × 240
=> 48kg
Hence, the 20% of 240kg will be 48kg.
(R S Aggarwal Quantitative Aptitude Free PDF)
Percentage Questions For Competitive Exam: Fraction values
Percentage is denoted by the symbol %. Percentage means per every 100 i.e. if we say 25% then it can be written as 25/100 and when you will simplify it then it becomes 1/4. In order to solve the percentage questions for competitive exam in less time candidates should learn some important fraction values of percentage. Any fraction can be converted into percentage by multiplying to 100. In the table given below candidates can check the fraction value of percentage.
Percentage Fraction Form
- 100% 1
- 50% 1/2
- 33+1/3% or 33.33 1/3
- 25% 1/4
- 16+2/3% or 16.66% 1/6
- 14+2/7% or 14.28% 1/7
- 12.5% 1/8
- 100/9% or 11.11% 1/9
- 10% 1/1
- 100/11 or 9.09% 1/11
- 81/3 % 1/12
Percentage Questions For Competitive Exam: Formulas
Before solving percentage questions for competitive exam candidates first checkout the percentage formulas given below(R S Aggarwal Quantitative Aptitude Free PDF)
Change in quantity: There are two types of changes occur when any number is increased or decreased from its original value and they are actual change as well as percentage change.
Actual Change– Rahul bought 1kg mangoes for rupees 150 in the month of April and next month the price gets increased and now it becomes 200. So here the price of the mangoes gets increased from 150 to 200 so the actual change would be(R S Aggarwal Quantitative Aptitude Free PDF)
Actual change: 200-150= 50
Percentage change: Now lets suppose if we have to calculate the price change in percentage then it would be calculated by the given below formula
Actual change/original value*100
50/200*100= 25%
To calculate x% of y – (x/100) * y = (x*y)/100
x% of y = y% of x
Increase A by x%= A(1 + x/100)
Decrease A by x% = A(1 – x/100)(R S Aggarwal Quantitative Aptitude Free PDF)
If Y is x% more /less than Z, then Z is 100x/(100 + x) % less/more than Y
Successive Percentage Change – If there are successive percentage increases of x % and y%, the effective percentage increase is: {(x + y + (xy/100)}%
SS Bharti Maths Notes PDF for SSC CGL
Percentage Questions For Competitive Exam
The major concern which remains in the candidate’s mind is whether the percentage questions are different for every competitive exam. Well the topic is common but candidates need to be exam oriented as the level of question varies exam wise. Some of the percentage questions for competitive exam is given below and for more questions candidates can give free quizzes which are available on adda247 app.(R S Aggarwal Quantitative Aptitude Free PDF)
Q1. Nandita scored 80% marks in five subjects together Hindi, Science, Mathematics, English and Sanskrit, where the maximum marks of each subject were 105. How many marks did Nandita scored in Science, if she scored 89 marks in hindi 92 marks in Sanskrit, 98 marks in Mathematics and 81 marks in English?
(a) 60
(b) 75
(c) 65
(d) 70
(e) 80
Q2. A number is divided into two parts in such a way that 80% of 1st part is 3 more than 60% of 2nd part and 80% of 2nd part is 6 more than 90% of the 1st part. Then the number is:(R S Aggarwal Quantitative Aptitude Free PDF)
(a) 125
(b) 130
(c) 135
(d) 145
(e) 155
Q3. The expenses on rice, fish and oil of a family are in the ratio 12 : 17 : 3 respectively. The price of these articles is increased by 20%, 30% and 50% respectively. The total expenses increased by:(R S Aggarwal Quantitative Aptitude Free PDF)
(a) 113/8 %
(b) 57/8 %
(c) 449/8 %
(d) 225/8 %
(e) None of these
Q4. The cost of a piece of diamond varies with the square of its weight. A diamond of Rs. 5184 value is cut into 3 pieces whose weights are in the ratio 1 : 2 : 3. Find the loss involved in the cutting.(R S Aggarwal Quantitative Aptitude Free PDF)
(a) Rs. 3068
(b) Rs. 3088
(c) Rs. 3175
(d) Rs. 3168
(e) None of these
(R S Aggarwal Quantitative Aptitude Free PDF)
Q5. The total strength of capital Education is 5000. The number of males and females increases by 8% and 16% respectively and strength becomes 5600. What was the number of males at Capital Education?
(a) 2500
(b) 2000
(c) 3000
(d) 4000
(e) 4500
Q6. The rates of simple interest in two banks A and B are in the ratio 5 : 4. A person wants to deposit his total savings in these two banks in such a way that he receives equal half yearly interest from both. He should deposit the savings in banks A and B in the ratio:(R S Aggarwal Quantitative Aptitude Free PDF)
(a) 2 : 5
(b) 4 : 5
(c) 5 : 2
(d) 5 : 4
(e) 3 : 5
Q7. One year ago the ratio between Laxman’s and Gopal’s salary was 3 : 4. The ratios of their individual salaries between last year’s and this year’s salaries are 4 : 5 and 2 : 3 respectively. At present the total of their salary is Rs. 4160. The salary of Laxman, now is:(R S Aggarwal Quantitative Aptitude Free PDF)
(a) Rs. 1040
(b) Rs. 1600
(c) Rs. 2560
(d) Rs. 3120
(e) Rs. 4210
Percentage Questions For Competitive Exam
Q8. In a village, each of the 60% of families has a cow; each of the 30% of families has a buffalo and each of the 15% of families has both a cow and a buffalo. In all there are 96 families in the village. How many families do not have a cow or a buffalo?(R S Aggarwal Quantitative Aptitude Free PDF)
(a) 20
(b) 24
(c) 26
(d) 17
(e) 28
Q9. A businessman imported Laptop, worth Rs. 210000, Mobile phones worth Rs. 100000 and Television sets worth Rs. 150000. He had to pay 10% duty on Laptops, 8% on phones and 5% on Television sets as special case. How much total duty (in rupees) he had to pay on all items as per above details?
(a) 36500
(b) 37000
(c) 37250
(d) 37500
(e) 42500
Q10. 60% students of a college study math, 55% students study commerce and 15% students study both. If ratio of boys to girl who study math only is 3 : 2 and ratio of boys to girls who study commerce only is 2 : 3, then total number of boys who study only math and only commerce together is what percent of total number of girls who study only math and only commerce together? (in approximate)(R S Aggarwal Quantitative Aptitude Free PDF)
(a) 102%
(b) 109%
(c) 117%
(d) 123%
(e) 112%
Q11. Mr. Raghav owned a flat for Rs. 13.2 lacs. He spends 20% of his monthly salary on its paintings. 25% on lighting and furniture, 15% on foods and other supplements. If Mr. Raghav’s annual salary is 10.8 lacs then find the total spending made by Mr. Raghav.(R S Aggarwal Quantitative Aptitude Free PDF)
(a) 137.4 lacs
(b) 1.374 lacs
(c) 13.74 lacs
(d) 11.74 lacs
(e) 17.34 lacs
Q12. The entrance ticket of an exhibition was Rs. 5. Later it was decreased by 20% and thus the sale amount is increased by 44%. What was the percentage increase in the number of visitors?(R S Aggarwal Quantitative Aptitude Free PDF)
(a) 64%
(b) 24%
(c) 80%
(d) 20%
(e) 40%
Q13. A tree’s height increases annually by 1/8th of its height. By how much will its height increase after 2.5 years, if it stands today at 10 m height?(R S Aggarwal Quantitative Aptitude Free PDF)
(a)3 m
(b)3.44 m
(c)3.6 m
(d)3.88 m
(e)4 m
Q14. A number X is less than another number Y. Number Y is three fourth of 24. Find the sum of the two numbers X and Y.(R S Aggarwal Quantitative Aptitude Free PDF)
(a) 30
(b) 33
(c) 36
(d) 24
(e) 42
Q15. Udita purchased a hand bag in Rs. 2,520. Later she felt that she had given 5% extra of the actual price of hand bag. Find the actual price of hand bag.
(a) Rs. 2,646
(b) Rs. 2,500
(c) Rs. 2400
(d) Rs. 2,450
(e) None of these
Some Important Maths Questions:-
1. The value of log 10000 is-
(A) 4 (B) 8 (C) 5 (D) 1 (Ans : a)
Hint: log 10000 = log10 104=4(R S Aggarwal Quantitative Aptitude Free PDF)
2. A boy takes 20 minutes to reach the school at an average speed of 12 km/h. If he has to reach the school in 15 minutes, then the average speed should be…..
(A) 14 km/h (b) 15 km/h (c) 16 km/h (d) 18 km/h (Ans: c)
Hint: Distance of school =12×20/60=4 km
Now his speed=distance/time=4/15/60
=16 km/h
3.A man gave 1/4th of his property to his daughter, to his sons and 1/5 to charity. Accordingly, how much did he give in total?
(a) 1/20 (b) 19/20 (c) 1/10 (d) 9/10 (Ans : b)
Hint: Total part given by the person
=1/4+½+1/5=5+10+4/20=19/20
4. 15% of 220 =?
(A) 33 (B) 22 (C) 24 (D) 26 (Ans : a)
Hint: 220×15/100=33
5. 8888 + 888 + 88 + 8 = ?(R S Aggarwal Quantitative Aptitude Free PDF)
(A) 9784 (B) 9792 (C) 9072 (D) None of these (Ans : d)
6. Out of 450 apples, 30% are rotten. How many apples are fine?
(A) 135 (B) 140 (C) 125 (D) 315 (Ans : a)
Hint: Number of rotten apples = 30% of 450
= 450×30/100=135
7. A star is about 8.1×1013 km away from the earth. Suppose light travels at a speed of 3.0×105 km/s. Find the time taken by the light from the star to reach the earth.
(A) 2.7×108 (B) 2.7×1011 (C) 7.5×104 (D) 7.5×103 (Ans : a)
Hint: Time taken from star to type to reach Earth 1
= distance/speed = 8.1×1013/3.0×105 = 2.7×108 seconds
8. An article worth Rs. By selling it for 220, Neeta made a profit of 10%. Accordingly for how much should he sell it so that the profit becomes 30%?
(a) Rs. 220 (b) Rs. 230 (c) Rs. 260 (d) Rs. 280 (Ans : c)
Hint: Cost price of article =200 × 100/110 = Rs. 200
Selling price of article to make 30% profit
= 130% of 200 = Rs. 260(R S Aggarwal Quantitative Aptitude Free PDF)
9. 100 × 10 – 100 + 2000 » 100 is equal to?
(a) 20 (b) 920 (c) 980 (d) 1000 (Ans : b)
Hint: 100 × 10 – 100 + 2000 » 100
= 1000 – 100 + 20 = 900 + 20 = 920
10. If the side of a square is doubled, then the area-
(A) doubles (B) 4 times (C) 8 times (D) 16 times (Ans : b)
Hint: According to the question, A1=a2
A2=(2a)2=4a2
So obviously it will be four times.
maths gk questions and answers
1. Who invented the slide rule?
Answer: William Otrade
2. Who invented the moon?
Answer: Joseph Huddart(R S Aggarwal Quantitative Aptitude Free PDF)
3. Who discovered the center of gravity?
Answer: Archimedes
4. Where was the abacus invented?
Answer: China
5. The value of pi?
Answer: 3.14159(R S Aggarwal Quantitative Aptitude Free PDF)
6. The value of cos is 360°?
Answer 1
7. What is an angle greater than 180 degrees but less than 360 degrees called?
Answer: Reversible angle
8. Who discovered the laws of lever and pulley?
Answer: Archimedes
9. Scientist who was born on Pi Day?
Answer: Albert Einstein
10. Who discovered the Pythagorean theorem?
Answer: Pythagoras of Samosas
11. Who discovered the symbol infinity “∞”?
Answer: John Wallis(R S Aggarwal Quantitative Aptitude Free PDF)
12. Father of Algebra?
Answer: Muhammad ibn Musa al-Khwarizmi (Persian mathematician)
13. Who discovered the Fibonacci sequence?
Answer: Leonardo Pisano Bigolo
14. The first person to use the Greek letter pi (π) to denote a constant?
Answer: William Jones in 1706
15. Who discovered logarithm and decimal point?
Answer: John Napier
16. Who invented the equal sign (=)?
Answer: Robert Ricarde
17. Who is the father of mathematics?
Answer: Archimedes(R S Aggarwal Quantitative Aptitude Free PDF)
18. Who discovered Zero (0)?
Answer: Aryabhata, 458 AD
Explanation: Aryabhatta invented zero but he did not give any symbol for zero, Brahmagupta was the first to give the symbol of zero and the rules for counting with zero.
19. What is the average of the first 50 natural numbers?
Answer: 25.5
20. When is Pi Day celebrated across the world?
Answer: 14 March(R S Aggarwal Quantitative Aptitude Free PDF)
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