Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
What will come in place of question mark (?) in the following number series?
500, 501, 1004, 3015, 12064, ?
63250
603250
60325
503250
None of these
Correct answer
60325
Why this answer is correct
500 × 1 + 1 = 501
501 × 2 + 2 = 1004
1004 × 3 + 3 = 3015
3015 × 4 + 4 = 12064
By observing the pattern,
12064 × 5 + 5 = ?
⇒ ? = 60325
∴ The value of ? is 60325
What will come in place of question mark (?) in the following number series?
18, 21, 27, 39, ?, 111
63
36
66
60
None of these
Correct answer
63
Why this answer is correct
Calculation:
The series follows the following pattern
18 + 3 = 21
21 + 6 = 27
27 + 12 = 39
39 + 24 = 63
63 + 48 = 111
∴ The missing number is 63.
What will come in the place of the question mark ‘?’ in the following question?
2 , 7 , 14 , 24 , ? , 57
38
49
45
35
None of these
Correct answer
38
Why this answer is correct
Given:
2 , 7 , 14 , 24 , ? , 57
Calculation:
Difference between first and second number = 7 - 2 = 5
Difference between second and third number = 14 - 7 = 7
Difference between third and fourth number = 24 - 14 = 10
Difference of difference between (second and third, first and second) number = 7 - 5 = 2
Difference of difference between (third and fourth, second and third) = 10 - 7 = 3
As, we can see the numbers are in sequence of 2, 3, 4
∴ Next number is 24 + (10 + 4) = 38.
What will come in place of question mark (?) in the following number series?
400, 200, 100, ?, 25, 12.5
50
70
75
80
40
Correct answer
50
Why this answer is correct
Given:
The number series:
400, 200, 100, ?, 25, 12.5
Concept Used:
Number series following a fixed pattern.
Calculation;
The given number series follows the pattern:
400 × 0.5 = 200
200 × 0.5 = 100
100 × 0.5 = 50
50 × 0.5 = 25
25 × 0.5 = 12.5
∴ The number in place of “?” in the given number series is 50
What should come in place of the question mark '?' in the following number series?
1722, 2188, 2732, 3360, ?
4072
4081
4075
4084
4078
Correct answer
4078
Why this answer is correct
The correct answer is: 5
Given:
1722, 2188, 2732, 3360, ?
Calculation:
the series follows the following pattern:
123 - 6 = 1722
133 - 9 = 2188
143 - 12 = 2732
153 - 15 = 3360
163 - 18 = 4078
∴ 4078 will come in place of ?
What will come in place of question mark (?) in the following number series?
320, 162, 84, 46, 28, ?
16
22
14
18
20
Correct answer
20
Why this answer is correct
Calculation:
The pattern of the number series is-
⇒ 320 ÷ 2 + 2 =162
⇒ 162 ÷ 2 + 3 = 84
⇒ 84 ÷ 2 + 4 = 46
⇒ 46 ÷ 2 + 5 = 28
⇒ 28 ÷ 2 + 6 = 20
∴ The value of ? is 20
Kabir sold his old washing machine for Rs. 10500 which he bought 6 months before, on that washing machine he incurred a loss of 20%. To gain 20% profit at what price he needs to sell the washing machine.
16550
17240
18000
17650
15750
Correct answer
15750
Why this answer is correct
Shortcut Trick
Loss of 20% means Selling Price (SP1) = 100% − 20% = 80%.
Profit of 20% means New Selling Price (SP2) = 100% + 20% = 120%.
According to the question, 80% corresponds to Rs. 10500.
New SP (120%) = (10500 ÷ 80) × 120 = 10500 × (3 ÷ 2).
New SP = 5250 × 3 = 15750.
∴ The correct answer is Rs. 15750.
Alternate Method
Given → Initial SP = Rs. 10500, Initial Loss = 20%, Target Profit = 20%.
Formulas: CP = [SP × 100] ÷ [100 − Loss%]; New SP = [CP × (100 + Gain%)] ÷ 100.
⇒ Step 1: Calculate CP = (10500 × 100) ÷ (100 − 20) = (10500 × 100) ÷ 80 = Rs. 13125.
⇒ Step 2: Calculate New SP = 13125 × (120 ÷ 100) = 13125 × 1.2.
⇒ Step 3: New SP = Rs. 15750.
∴ The correct answer is Rs. 15750.
Additional Information
Cost Price (CP) and Selling Price (SP)
CP is the price at which an article is purchased. SP is the price at which it is sold.
Profit and Loss Percentage
Profit% = (Profit ÷ CP) × 100. Loss% = (Loss ÷ CP) × 100. Both are always calculated on CP unless stated otherwise.
Directions: Study the following information carefully and answer the questions.
The line graph below shows the number of students studying in public school and in private schools in four cities P, Q , R and S.
Find the ratio between the total number of students (public + private) in City P, City Q, and City S together to the total number of students in private schools in City Q and City R together.
112: 53
123:18
173:31
151:14
None of these
Correct answer
173:31
Why this answer is correct
Compute total students in each required city:
City P total = Public + Private = 6400 + 3600 = 10000
City Q total = 8000 + 3000 = 11000
City S total = 9600 + 4000 = 13600
Sum of totals for P, Q and S:
⇒ 10000 + 11000 + 13600 = 34600
Total private students in Q and R:
Q (private) = 3000
R (private) = 3200
⇒ Sum = 3000 + 3200 = 6200
Required ratio:
⇒ (Total of P + Q + S) : (Private in Q + R) = 34600 : 6200 ⇒ 173 : 31
Hence, the correct answer is 173:31.
Directions: Study the following information carefully and answer the questions.
The line graph below shows the number of students studying in public school and in private schools in four cities P, Q , R and S.
The total number of students in public schools in City P and City R together is how much less than the total number of students (public + private) in City R and City S together?
6,200
38,000
10,400
29,100
None of these
Correct answer
10,400
Why this answer is correct
Given values:
Public School, City P = 6400
Public School, City R = 7200
Private School, City R = 3200
Public School, City S = 9600
Private School, City S = 4000
Compute totals:
Public (P + R) = 6400 + 7200 = 13600
Total (R public + R private) = 7200 + 3200 = 10400
Total (S public + S private) = 9600 + 4000 = 13600
Total (R + S) = 10400 + 13600 = 24000
Required difference:
Difference = 24000 − 13600 = 10400
Hence, the correct answer is 10,400.
Directions: Study the following information carefully and answer the questions.
The line graph below shows the number of students studying in public school and in private schools in four cities P, Q , R and S.
The total number of students in public schools in City Q and City S together is what percent of the total students in private schools in the same cities?
3 (169/11)%
251 (3/7)%
25 (50/13%
196 (1/5)%
None of these
Correct answer
251 (3/7)%
Why this answer is correct
Totals for Cities Q and S:
Public (Q) = 8000
Public (S) = 9600
⇒ Total Public (Q + S) = 8000 + 9600 = 17600
Private (Q) = 3000
Private (S) = 4000
⇒ Total Private (Q + S) = 3000 + 4000 = 7000
Required percentage:
Percentage = (Total Public (Q+S) ÷ Total Private (Q+S)) × 100
⇒ (17600 ÷ 7000) × 100 = (176 ÷ 70) × 100 = (88 ÷ 35) × 100
⇒ 88 × 100 ÷ 35 = 8800 ÷ 35 ≈ 251.43%
Hence, the correct answer is 251 (3/7)%.
Directions: Study the following information carefully and answer the questions.
The line graph below shows the number of students studying in public school and in private schools in four cities P, Q , R and S.
Out of the total students in public and private schools in City R, 54% and 28% respectively were awarded for their performances. Find the total percentage of students in City R who were not awarded for their performances.
54%
57%
48%
49%
56%
Correct answer
54%
Why this answer is correct
City R:
Public school students = 7200
Private school students = 3200
Awarded in Public school = 54% of 7200
Awarded in Private school = 28% of 3200
Awarded (Public) = 54% × 7200 = 0.54 × 7200 = 3888
Awarded (Private) = 28% × 3200 = 0.28 × 3200 = 896
Total Awarded = 3888 + 896 = 4784
Total students in City R = 7200 + 3200 = 10400
Not awarded = 10400 − 4784 = 5616
Percentage not awarded = (5616 ÷ 10400) × 100 = 0.54 × 100 = 54%
Hence, the correct answer is 54%.
Directions: Study the following information carefully and answer the questions.
The line graph below shows the number of students studying in public school and in private schools in four cities P, Q , R and S.
Find the average number of students in private schools across all four cities.
3450
3780
3810
3920
3640
Correct answer
3450
Why this answer is correct
Private school students:
P = 3600
Q = 3000
R = 3200
S = 4000
Total private school students = 3600 + 3000 + 3200 + 4000 = 13,800
Average = Total ÷ 4 = 13,800 ÷ 4 = 3,450
Hence, the correct answer is 3,450.
There are 37 students in a class and the average of the age of the class is 16 years. If the age of the lady teacher is also included then the average increased by 6 months. Find the age of the lady teacher.
33 years
34 years
36 years
35 years
37 years
Correct answer
35 years
Why this answer is correct
Shortcut Trick
Age of Teacher = Original Average + (New Total Members × Increase in Average)
Total students = 37; After teacher joins, Total members = 37 + 1 = 38
Increase in average = 6 months = 0.5 years
⇒ Teacher age = 16 + (38 × 0.5) = 16 + 19 = 35 years
∴ The correct answer is 35 years.
Alternate Method
Given: Number of students = 37; Average age = 16 years; New Average = 16.5 years.
Formula: Total Sum = Average × Number of items
⇒ Total age of 37 students = 37 × 16 = 592 years
⇒ Total members including teacher = 37 + 1 = 38
⇒ New average = 16 years + 6 months = 16.5 years
⇒ Total age of 38 members = 38 × 16.5 = 627 years
⇒ Age of Lady Teacher = Total (38) − Total (37)
⇒ Age = 627 − 592 = 35 years
∴ The correct answer is 35 years.
Additional Information
Inclusion/Exclusion Rule
When a new person joins and the average increases, the new person age = Old Average + (New Total Count × Rise in Average).
Weighted Average
Used when two groups are combined: Combined Average = (n1x1 + n2x2) ÷ (n1 + n2).
Speed of boat A travelling in still water is 15 km/hr. Speed of boat B is 40% of twice of speed of boat A in still water. A is travelling upstream and B is travelling downstream, find the time(in hours) for boats to meet if the river is 108 km long.
2
3
4
none of these
cannot be determined
Correct answer
4
Why this answer is correct
Shortcut Trick
Speed of Boat A in still water (uA) = 15 km/hr
Speed of Boat B in still water (uB) = 40% of (2 × 15) = 12 km/hr
When one boat travels upstream and the other travels downstream, the relative speed of the boats is simply the sum of their speeds in still water, because the stream speed (v) cancels out: (uA − v) + (uB + v) = uA + uB = 15 + 12 = 27 km/hr
Meeting time = Distance ÷ Relative Speed = 108 ÷ 27 = 4 hours
∴ The correct answer is 4 hours.
Alternate Method
Given:
Speed of boat A in still water (uA) = 15 km/hr
Speed of boat B in still water (uB) = 40% of (2 × 15) = 0.40 × 30 = 12 km/hr
Total distance between boats = 108 km
Let the speed of the stream be v km/hr.
Formula Used:
Upstream speed of Boat A = uA − v = 15 − v
Downstream speed of Boat B = uB + v = 12 + v
Relative speed = Speed of A + Speed of B
Time to meet = Total Distance ÷ Relative Speed
Calculations:
⇒ Relative Speed = (15 − v) + (12 + v)
⇒ Relative Speed = 15 + 12 = 27 km/hr
⇒ Time to meet = 108 ÷ 27
⇒ Time to meet = 4 hours
∴ The correct answer is 4 hours.
Additional Information
Relative Speed in Rivers
When two boats move towards each other, one going upstream and the other going downstream, the effect of the stream speed cancels out completely. The relative speed is simply the sum of their individual speeds in still water (u1 + u2).
Upstream and Downstream Formulas
Downstream speed (D) = u + v and Upstream speed (U) = u − v, where u is the speed of the boat in still water and v is the speed of the stream.
Finding Boat and Stream Speeds
Speed of boat in still water u = (D + U) ÷ 2, and Speed of stream v = (D − U) ÷ 2.
Find the approximate value of x in the following question.
x2 - (6.11 × 56.13) = (28.9 × 36.02) + (47.8 × 32.2)
42
62
54
48
64
Correct answer
54
Why this answer is correct
Solution:
x2 - (6.11 × 56.13) = (28.9 × 36.02) + (47.8 × 32.2)
x2 - (6 × 56) = (29 × 36 + 48 × 32)
x2 - 336 = 1044 + 1536
x2 - 336 = 2580
x2 = 2580 + 336
x2 = 2916
x = √2916
x = 54
What approximate value should come in place the of question mark ? in the following question?
3.038 × 2.934 ÷ 242.93 = 9.03 × 3.03 × 80.99 × 2.994 ÷ ?
3
9
27
81
243
Correct answer
81
Why this answer is correct
Given expression is,
3.038 × 2.934 ÷ 242.93 = 9.03 × 3.03 × 80.99 × 2.994 ÷ ?
We can write the given values as:
3.03, 2.93 and 2.99 ≈ 3, 242.93 ≈ 243
9.03 ≈ 9 and 80.99 ≈ 81
Given expression is:
⇒ 38 × 34 ÷ 243 = 9 × 3 × 81 × 34 ÷ ?
⇒ 38 × 34 ÷ 35 = 32 × 3 × 34 × 34 ÷ ?
⇒ 3(8 + 4 – 5) = 3(2 + 1 + 4 + 4) ÷ ?
⇒ 37 = 311 ÷ ?
⇒ ? = 311 ÷ 37
⇒ ? = 3(11 – 7)
⇒ ? = 34
⇒ ? = 81
What should come in place of question mark (?) in the following questions? (You do not have to calculate the exact value.)
99.67 + 202.15 ÷ 1.97 – 32.20 = ?% of 1300.03
2
18
11
13
20
Correct answer
13
Why this answer is correct
Rules of Approximation:
Concept:
Follow BODMAS rule to solve this question, as per the order given below-
Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first and following BODMAS rule in the bracket-
Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.
Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.
Step - 4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.
Since we need to find out the approximate value, we can write these values to their nearest integers.
Calculation:
Given Expression,
99.67 + 202.15 ÷ 1.97 – 32.20 = ?% of 1300.03
We can also write values as:
99.67 ≈ 100, 202.15 ≈ 202, 1.97 ≈ 2, 32.20 ≈ 32, 1300.03 ≈ 1300
Given expression becomes,
⇒ 100 + 202 ÷ 2 – 32 = ?% of 1300
⇒ 100 + 101 – 32 = ?% of 1300
⇒ 201 – 32 = ?% of 1300
⇒ 169 = ?% of 1300
⇒ ? = (169 × 100)/1300
⇒ ? ≈ 13
What approximate value should come in place of the question mark (?) in the following question?
(484.30 ÷ 11.11) × 4.87 – 5.85 % of 700 = ? × 2.01 + 4.4
80
89
91
60
87
Correct answer
87
Why this answer is correct
Follow BODMAS rule to solve this question, as per the order given below,
Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,
Step-2- Any mathematical 'Of' or 'Exponent' must be solved next,
Step-3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,
Step-4- Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.
Given Expression,
(484.30 ÷ 11.11) × 4.87 – 5.85 % of 700 = ? × 2.01 + 4.4
We can also write values as:
484.30 ≈ 484, 11.11 ≈ 11, 4.87 ≈ 5, 2.01 ≈ 2, 4.4 ≈ 4, 5.85 ≈ 6
Given expression becomes,
⇒ (484 ÷ 11) × 5 – 6 % of 700 = ? × 2 + 4
⇒ 44 × 5 – 6/100 × 7 = ? × 2 + 4
⇒ 220 – 42 = ? × 2 + 4
⇒ 178 = ? × 2 + 4
⇒ ? × 2 = 174
⇒ ? ≈ 87
Find the approximate value which should replace the question mark (?) in the following question.
√1765 ÷ √200 + (12.02 × 1.99 × 7.09)] = ? × 3 – 12
51
61
71
81
41
Correct answer
61
Why this answer is correct
Follow BODMAS rule to solve this question, as per the order given below,
Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,
Step-2- Any mathematical 'Of' or 'Exponent' must be solved next,
Step-3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,
Step-4- Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.
Given expression is,
√1765 ÷ √200 + (12.02 × 1.99 × 7.09)] = ? × 3 – 12
Taking Approximate values,
√1765 ≈ √1764, √200 ≈ √196, 12.02 ≈ 12, 1.99 ≈ 2, 7.09 ≈ 7
⇒ 42 ÷ 14 + (12 × 2 × 7) = ? × 3 – 12
⇒ 3 × ? = 171 + 12 = 183
∴ ? = 61
Kamal and Raju started a partnership for total of 3.5 years in such a way that initially Kamal invested Rs. 7500 for 24 months after that Kamal withdraws his amount and Raju invests certain capital for the remaining time. The profit Raju received after 3.5 years is Rs. 1400 out of total profit of Rs. 3000.What was the amount Raju invested.
Rs. 9000
Rs. 7500
Rs. 8400
Rs. 8750
Rs. 8000
Correct answer
Rs. 8750
Why this answer is correct
Shortcut Trick
Profit ratio Kamal : Raju = (3000 − 1400) : 1400 = 1600 : 1400 = 8 : 7.
Time ratio = 24 months : (42 − 24) months = 24 : 18 = 4 : 3.
Investment ratio = (Profit ÷ Time) ⇒ (8 ÷ 4) : (7 ÷ 3) = 2 : 7/3 = 6 : 7.
Since 6 units = Rs. 7500, then 1 unit = Rs. 1250.
Raju investment = 7 × 1250 = Rs. 8750.
∴ The correct answer is Rs. 8750.
Alternate Method
Given → Kamal Investment (Ck) = Rs. 7500, Time (Tk) = 24 months. Total time = 3.5 years = 42 months. Raju Time (Tr) = 42 − 24 = 18 months. Total profit = Rs. 3000, Raju Profit (Pr) = Rs. 1400.
Formulas: Profit Ratio = (Investment1 × Time1) : (Investment2 × Time2)
Steps:
⇒ Profit of Kamal (Pk) = Total Profit − Raju Profit = 3000 − 1400 = Rs. 1600.
⇒ Ratio of profits (Pk / Pr) = (Ck × Tk) / (Cr × Tr).
⇒ 1600 / 1400 = (7500 × 24) / (X × 18).
⇒ 8 / 7 = (7500 × 4) / (X × 3).
⇒ 8 × 3 × X = 7 × 7500 × 4.
⇒ 24X = 210000.
⇒ X = 210000 / 24 = Rs. 8750.
∴ The correct answer is Rs. 8750.
Additional Information
Partnership Basic Concept
In a partnership, the profit is distributed among partners in the ratio of the product of their invested capital and the duration of investment.
Investment Calculation
If profits and time periods are known, the investment ratio can be found by Investment = Profit ÷ Time.
Solving previous year questions by topic helps identify recurring concepts, question patterns, and frequently asked sub-topics. Attempt each question, review the step-by-step explanation, and note down key formulas or facts for quick revision before the exam.