Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
What should come in place of the question mark '?' in the following number series?
81, 99, 123, 153, 189, ?
221
211
241
101
231
Correct answer
231
Why this answer is correct
The series follows the following pattern:
81 + 18 = 99
99 + 24 = 123
123 + 30 = 153
153 + 36 = 189
189 + 42 = 231
What should come in place of the question mark '?' in the following number series?
26, 38, 52, ?, 86, 106
68
72
62
66
76
Correct answer
68
Why this answer is correct
The series follows the following pattern:
52 + 1 = 26
62 + 2 = 38
72 + 3 = 52
82 + 4 = 68
92 + 5 = 86
102 + 6 = 106
What should come in place of the question mark '?' in the following number series?
12, 15, 24, 39, 60, ?
77
81
83
87
91
Correct answer
87
Why this answer is correct
The series follows the following pattern:
12 + 3 = 15
15 + 9 = 24
24 + 15 = 39
39 + 21 = 60
60 + 27 = 87
What will come in the place of question mark(?) in the following series?
6, 17, ?, 28,-16, 39
18
-18
5
-5
21
Correct answer
-5
Why this answer is correct
Calculations:
The series follows the following pattern:
6 + 11 = 17
17 – 22 = -5
-5 + 33 = 28
28 – 44 = -16
-16 + 55 =39
∴ The missing term in the series is -5.
What should come in place of question mark (?) in the following number series?
310, 382, 474, ?, 726, 890
480
458
588
580
None of these
Correct answer
588
Why this answer is correct
The series follows the following pattern
∴ The missing number = 588
In Gada Electronics, the profit is 420% on cost price of Television. If the cost price is increased by 35% but the selling price does not change, what percent of the selling price will be the profit nearly
70
80
74
50
65
Correct answer
74
Why this answer is correct
Shortcut Trick
Assume initial Cost Price (CP) = 100. Profit = 420, so Selling Price (SP) = 100 + 420 = 520.
New CP = 100 + 35% of 100 = 135. SP remains constant at 520.
New Profit = 520 − 135 = 385.
Profit percentage on SP = (385 ÷ 520) × 100 ≈ 74%.
∴ The correct answer is 74%.
Alternate Method
Given → Profit% on CP = 420% | Increase in CP = 35% | SP is constant.
Formulas: Profit = SP − CP | Profit% on SP = (Profit ÷ SP) × 100.
⇒ Let initial CP = 100.
⇒ Profit = 420% of 100 = 420.
⇒ SP = CP + Profit = 100 + 420 = 520.
⇒ New CP = 100 + 35 = 135.
⇒ New Profit = SP − New CP = 520 − 135 = 385.
⇒ Profit percentage on SP = (385 ÷ 520) × 100 = 74.038% ≈ 74%.
∴ The correct answer is 74%.
Additional Information
Profit on Selling Price vs Cost Price
Standard profit% is always calculated on CP. However, some problems specifically ask for Profit% on Selling Price, where the denominator becomes SP instead of CP.
Effect of Constant Selling Price
When SP is fixed and CP increases, the absolute profit decreases, and the profit margin (whether based on CP or SP) also decreases accordingly.
Ratio between the present age of Ranita and Rahul is 3 ∶ 4. If sum of their ages is 63, what is the ratio between the age of Ranita and Rahul after 5 years?
14 ∶ 43
30 ∶ 11
32 ∶ 41
15 ∶ 31
40 ∶ 21
Correct answer
32 ∶ 41
Why this answer is correct
Shortcut Trick
Total ratio parts = 3 + 4 = 7 units
7 units = 63 years → 1 unit = 9 years
Ranita's current age = 3 × 9 = 27 years | Rahul's current age = 4 × 9 = 36 years
Ages after 5 years → Ranita: 27 + 5 = 32 | Rahul: 36 + 5 = 41
∴ The correct answer is 32 ∶ 41.
Alternate Method
Given: Present ratio = 3 ∶ 4, Sum = 63 years, Time offset = +5 years.
⇒ Let the present ages be 3x and 4x.
⇒ 3x + 4x = 63
⇒ 7x = 63
⇒ x = 9
⇒ Ranita's present age = 3 × 9 = 27 years
⇒ Rahul's present age = 4 × 9 = 36 years
⇒ Age after 5 years: Ranita = 32, Rahul = 41
⇒ Required Ratio = 32 ∶ 41
∴ The correct answer is 32 ∶ 41.
Additional Information
Ratio and Proportion in Ages
The difference between the ages of two people remains constant throughout their lives. If the ratio changes, the unit difference should be normalized.
Sum of Ages Shortcut
Value of one ratio part = Total Sum ÷ Sum of Ratio parts. Multiply this value with individual parts to find specific ages.
In a mixture of 80 litres, milk and water were in the ratio of 2 : 3. If 25% of the mixture is replaced with the same amount of milk, then what is the amount of milk in the final mixture?
44 litres
46 litres
54 litres
56 litres
None of these
Correct answer
44 litres
Why this answer is correct
Shortcut Trick
Initial milk in 80 L (ratio 2:3) = 80 × (2/5) = 32 L.
Mixture replaced = 25% of 80 L = 20 L.
Milk removed = 25% of 32 L = 8 L.
Milk added = 20 L (equal to the mixture removed).
Final Milk = 32 − 8 + 20 = 44 L.
∴ The correct answer is 44 litres.
Alternate Method
Given: Total Mixture = 80 L, Ratio (M:W) = 2:3.
⇒ Initial Milk = (2/5) × 80 = 32 L.
⇒ Initial Water = (3/5) × 80 = 48 L.
⇒ Replacement amount = 25% of 80 = 20 L.
⇒ Milk in 20 L mixture = (2/5) × 20 = 8 L.
⇒ Milk left after removal = 32 − 8 = 24 L.
⇒ Milk added = 20 L.
⇒ Final amount of Milk = 24 + 20 = 44 L.
∴ The correct answer is 44 litres.
Additional Information
Mixture Replacement Rule
When a part of a mixture is replaced by one of its components, the ratio of the components in the remaining part stays the same as the original ratio.
Formula for Remaining Quantity
Remaining amount of original liquid = Initial amount × (1 − x/V)n, where x is quantity replaced, V is total volume, and n is number of operations.
Alligation in Replacement
Replacement problems can also be solved by treating the added pure component as a 100% concentration mixture.
Directions: The following caselet shows the number of bikes and cars sold in the four different companies A, B, C and D.
Number of bikes sold in company A is 2.5 times of the number of cars sold in the same company. Number of cars sold in company A to B are in the ratio 5: 7 Number of bikes sold in company C is 500 more than the number of bikes sold in company A. Number of bikes sold in company B is 20% more than the number of bikes sold in company A. Total bikes sold in all the companies are 5850. Number of bikes sold in company D is 150 less than the number of bikes sold in company B. Number of cars sold in company C is 100 more than the number of cars sold in company D. Number of cars sold in company D is 350 less than the number of bikes sold in company D.
Number of bikes sold in company C is what percentage of the number of cars sold in all the companies.
50.77%
51.89%
53.03%
57.89%
50.89%
Correct answer
53.03%
Why this answer is correct
General Solution:
Number of cars sold in the company A = 5x
Number of cars sold in the company B = 7x
Number of bikes sold in the company A = 12.5x
Number of bikes sold in company C = 12.5x + 500
Number of bikes sold in company B = 12.5x × (120/100) = 15x
Number of bikes sold in company D = 15x - 150
12.5x + 12.5x + 500 + 15x + (15x - 150) = 5850
55x = (5850 - 350)
55x = 5500
x = 100
Number of cars sold in company A = 5 × 100 = 500
Number of cars sold in company B = 7 × 100 = 700
Number of bikes sold in company A = 12.5 × 100 = 1250
Number of bikes sold in company B = 15 × 100 = 1500
Number of bikes sold in company C = 1250 + 500 = 1750
Number of bikes sold in company D = 15 × 100 - 150 = 1350
Number of cars sold in company D = 1350 - 350 = 1000
Number of cars sold in company C = 1100
| Name of the company | Cars | Bikes |
|---|---|---|
| A | 500 | 1250 |
| B | 700 | 1500 |
| C | 1100 | 1750 |
| D | 1000 | 1350 |
Solution:
Number of bikes sold in company C = 1750
Number of cars sold in all the companies = (500+ 700 + 1100 + 1000) = 3300
Required percentage = 1750/3300 × 100 = 53.03%
Directions: The following caselet shows the number of bikes and cars sold in the four different companies A, B, C and D.
Number of bikes sold in company A is 2.5 times of the number of cars sold in the same company. Number of cars sold in company A to B are in the ratio 5: 7 Number of bikes sold in company C is 500 more than the number of bikes sold in company A. Number of bikes sold in company B is 20% more than the number of bikes sold in company A. Total bikes sold in all the companies are 5850. Number of bikes sold in company D is 150 less than the number of bikes sold in company B. Number of cars sold in company C is 100 more than the number of cars sold in company D. Number of cars sold in company D is 350 less than the number of bikes sold in company D.
Find the ratio between the number of cars sold in company C and D to the number of bikes sold in company A and D.
24: 23
28: 25
21: 26
19: 23
19: 17
Correct answer
21: 26
Why this answer is correct
General Solution:
Number of cars sold in the company A = 5x
Number of cars sold in the company B = 7x
Number of bikes sold in the company A = 12.5x
Number of bikes sold in company C = 12.5x + 500
Number of bikes sold in company B = 12.5x × (120/100) = 15x
Number of bikes sold in company D = 15x - 150
12.5x + 12.5x + 500 + 15x + (15x - 150) = 5850
55x = (5850 - 350)
55x = 5500
x = 100
Number of cars sold in company A = 5 × 100 = 500
Number of cars sold in company B = 7 × 100 = 700
Number of bikes sold in company A = 12.5 × 100 = 1250
Number of bikes sold in company B = 15 × 100 = 1500
Number of bikes sold in company C = 1250 + 500 = 1750
Number of bikes sold in company D = 15 × 100 - 150 = 1350
Number of cars sold in company D = 1350 - 350 = 1000
Number of cars sold in company C = 1100
| Name of the company | Cars | Bikes |
|---|---|---|
| A | 500 | 1250 |
| B | 700 | 1500 |
| C | 1100 | 1750 |
| D | 1000 | 1350 |
Solution:
Number of cars sold in company C = 1100
Number of cars sold in company D = 1000
Number of bikes sold in company A = 1250
Number of bikes sold in company D = 1350
Required ratio = (1000 + 1100): (1250 + 1350) = 2100: 2600 = 21: 26
Directions: The following caselet shows the number of bikes and cars sold in the four different companies A, B, C and D.
Number of bikes sold in company A is 2.5 times of the number of cars sold in the same company. Number of cars sold in company A to B are in the ratio 5: 7 Number of bikes sold in company C is 500 more than the number of bikes sold in company A. Number of bikes sold in company B is 20% more than the number of bikes sold in company A. Total bikes sold in all the companies are 5850. Number of bikes sold in company D is 150 less than the number of bikes sold in company B. Number of cars sold in company C is 100 more than the number of cars sold in company D. Number of cars sold in company D is 350 less than the number of bikes sold in company D.
Number of bikes sold in company E is 250 more than the number of bikes sold in company D and the number of cars sold in company E is 125 more than the number of cars sold in company C. Find the total number of vehicles (Cars + Bikes) sold in company E.
2195
2885
2765
2825
2655
Correct answer
2825
Why this answer is correct
General Solution:
Number of cars sold in the company A = 5x
Number of cars sold in the company B = 7x
Number of bikes sold in the company A = 12.5x
Number of bikes sold in company C = 12.5x + 500
Number of bikes sold in company B = 12.5x × (120/100) = 15x
Number of bikes sold in company D = 15x - 150
12.5x + 12.5x + 500 + 15x + (15x - 150) = 5850
55x = (5850 - 350)
55x = 5500
x = 100
Number of cars sold in company A = 5 × 100 = 500
Number of cars sold in company B = 7 × 100 = 700
Number of bikes sold in company A = 12.5 × 100 = 1250
Number of bikes sold in company B = 15 × 100 = 1500
Number of bikes sold in company C = 1250 + 500 = 1750
Number of bikes sold in company D = 15 × 100 - 150 = 1350
Number of cars sold in company D = 1350 - 350 = 1000
Number of cars sold in company C = 1100
| Name of the company | Cars | Bikes |
|---|---|---|
| A | 500 | 1250 |
| B | 700 | 1500 |
| C | 1100 | 1750 |
| D | 1000 | 1350 |
Solution:
Number of bikes sold in the company D = 1350
Number of cars sold in the company E = 1350 + 250 = 1600
Number of cars sold in the company C = 1100
Number of cars sold in the company E = 1100 + 125 = 1225
Total number of vehicles sold in the company E = (1600 + 1225) = 2825
Directions: The following caselet shows the number of bikes and cars sold in the four different companies A, B, C and D.
Number of bikes sold in company A is 2.5 times of the number of cars sold in the same company. Number of cars sold in company A to B are in the ratio 5: 7 Number of bikes sold in company C is 500 more than the number of bikes sold in company A. Number of bikes sold in company B is 20% more than the number of bikes sold in company A. Total bikes sold in all the companies are 5850. Number of bikes sold in company D is 150 less than the number of bikes sold in company B. Number of cars sold in company C is 100 more than the number of cars sold in company D. Number of cars sold in company D is 350 less than the number of bikes sold in company D.
If the number of cars sold in company A is increased by 25% and the number of bikes sales is increased by x. If the number of vehicles (Bikes + Cars) sold in company A is 2225 then find the number of bikes sales increased in company A.
325
300
350
200
250
Correct answer
350
Why this answer is correct
General Solution:
Number of cars sold in the company A = 5x
Number of cars sold in the company B = 7x
Number of bikes sold in the company A = 12.5x
Number of bikes sold in company C = 12.5x + 500
Number of bikes sold in company B = 12.5x × (120/100) = 15x
Number of bikes sold in company D = 15x - 150
12.5x + 12.5x + 500 + 15x + (15x - 150) = 5850
55x = (5850 - 350)
55x = 5500
x = 100
Number of cars sold in company A = 5 × 100 = 500
Number of cars sold in company B = 7 × 100 = 700
Number of bikes sold in company A = 12.5 × 100 = 1250
Number of bikes sold in company B = 15 × 100 = 1500
Number of bikes sold in company C = 1250 + 500 = 1750
Number of bikes sold in company D = 15 × 100 - 150 = 1350
Number of cars sold in company D = 1350 - 350 = 1000
Number of cars sold in company C = 1100
| Name of the company | Cars | Bikes |
|---|---|---|
| A | 500 | 1250 |
| B | 700 | 1500 |
| C | 1100 | 1750 |
| D | 1000 | 1350 |
Solution:
Number of cars sold in company A = 500 × (125/100) = 625
Number of vehicles sold = 2225
Number of bikes sold in company A = 2225 - 625 = 1600
Number of bike sold sales increased = (1600 - 1250) = 350
What will come in place of question mark (?) in the following equation?
1260 ÷ 42 × {(102 - 86) + 5} = ?
630
570
540
510
590
Correct answer
630
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
⇒ 1260 ÷ 42 × {(102 - 86) + 5} = ?
⇒ 1260 ÷ 42 × {(16 + 5} = ?
⇒ 1260 ÷ 42 × 21 = ?
⇒ 30 × 21 = ?
∴ ? = 630
What will come in place of question mark (?) in the following equation?
126.06 + 181.92 - 229.99 = 65.99 + ?
12
15
22
25
19
Correct answer
12
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
126.06 + 181.92 - 229.99 = 65.99 + ?
⇒ 308 - 230 = 66 + ?
⇒ 78 = 66 + ?
⇒ 78 - 66 = ?
∴ ? = 12
What will come in place of question mark (?) in the following equation?
1024 ÷ 128 + 24% of 250 = ?2 + 180 ÷ 45
44
64
80
14
8
Correct answer
8
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
1024 ÷ 128 + 24% of 250 = ?2 + 180 ÷ 45
⇒ 8 + 60 = ?2 + 4
⇒ 68 = ?2 + 4
⇒ ?2 = 64
⇒ ? = 8
What will come in place of question mark (?) in the following equation?
45% of 900 + 55% of 700 = 66% of 400 + ?
374
424
472
526
556
Correct answer
526
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
45% of 900 + 55% of 700 = 66% of 400 + ?
⇒ 405 + 385 = 264 + ?
⇒ ? = 405 + 385 - 264
⇒ ? = 526
What will come in place of question mark (?) in the following equation?
950 + 50 × 15 - 14 × 22 + √? = 113 + 92
200
240
320
400
420
Correct answer
400
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
950 + 50 × 15 - 14 × 22 + √? = 113 + 92
⇒ 950 + 750 - 308 + √? = 1331 + 81
⇒ 1392 + √? = 1412
⇒ √? = 20
⇒ ? = 400
What will come in place of question mark (?) in the following equation?
55% of 240 + 83 × 4 – 24 × 8 = ?
1788
1498
1678
1988
1828
Correct answer
1988
Why this answer is correct
55% of 240 + 83 × 4 – 24 × 8 = ?
⇒ 132 + 512 × 4 – 24 × 8 = ?
⇒ 132 + 512 × 4 – 24 × 8 = ?
⇒ 132 + 2048 – 192 = ?
⇒ 2180 – 192 = ?
∴ ? = 1988
What will come in place of question mark (?) in the following equation?
(25 × 30) – (110 × 8) + 670 = ? × 9
90
30
60
45
120
Correct answer
60
Why this answer is correct
(25 × 30) – (110 × 8) + 670 = ? × 9
⇒ 750 – 880 + 670 = ? × 9
⇒ 1420 – 880 = ? × 9
⇒ 540 = ? × 9
∴ ? = 60
What will come in place of question mark (?) in the following equation?
(96 + 48 × 5) ÷ 24 + 32 = ?
52
48
42
38
46
Correct answer
46
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
(96 + 48 × 5) ÷ 24 + 32 = ?
⇒ (96 + 240) ÷ 24 + 32 = ?
⇒ 336 ÷ 24 + 32 = ?
⇒ 14 + 32 = ?
∴ ? = 46
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.