IBPS RRB Clerk Prelims 2025 Numerical Ability Questions with Solutions

Explanation

The pattern of the series is formed by multiplying terms by consecutive integers: 2 × 2 = 4 4 × 3 = 12 12 × 4 = 48 48 × 5 = 240 240 × 6 = 1440 The missing value is 48.

Explanation

The pattern of multiplication factors between terms increases by 0.25 at each step: 1200 × 0.25 = 300 300 × 0.50 = 150 150 × 0.75 = 112.5 112.5 × 1.00 = 112.5 112.5 × 1.25 = 140.625 The missing value is 112.5.

Explanation

The sequence subtracts decreasing cubes and squares alternatively: 1600 - 8³ = 1600 - 512 = 1088 1088 - 7² = 1088 - 49 = 1039 1039 - 6³ = 1039 - 216 = 823 823 - 5² = 823 - 25 = 798 798 - 4³ = 798 - 64 = 734 The missing value is 734.

Explanation

The differences between successive terms are consecutive prime numbers in increasing order from right to left: 59 - 28 = 31 88 - 59 = 29 111 - 88 = 23 130 - 111 = 19 147 - 130 = 17 The missing value is 130.

Explanation

The primary differences between consecutive terms are 24, 31, 40, 51, 64, and 79. The differences of these differences (second differences) form a pattern decreasing by 2: 31 - 24 = 7 40 - 31 = 9 51 - 40 = 11 64 - 51 = 13 79 - 64 = 15 Adding 24 to 148 gives 172, and adding 31 to 172 gives 203. The missing value is 172.

Explanation

Simplifying the expression on the left-hand side by following the standard order of operations: First, perform addition and subtraction from left to right: 50 - 45 + 145 = 5 + 145 = 150

Now, set up the equation with the right-hand side expression: 150 = 2.5 × ?

To isolate the unknown quantity ?, divide 150 by 2.5: ? = 150 / 2.5 = 1500 / 25 = 60

Explanation

Evaluating the square roots on the left-hand side of the given equation: √225 = 15 and √25 = 5

Substituting these values into the left-hand side expression and applying division followed by multiplication: (15 ÷ 5) × 6 = 3 × 6 = 18

Now evaluating the right-hand side expression: ?% of 200 = (? / 100) × 200 = 2 × ?

Equating the left-hand side and right-hand side expressions: 18 = 2 × ? ? = 18 / 2 = 9

Explanation

Simplifying each term on the left-hand side of the given equation: 16 × 25 = 400 (25)² = 625

Combining all terms on the left-hand side: 400 + 280 - 625 = 680 - 625 = 55

The right-hand side represents 25% of the unknown number ?, which simplifies to: 25% of ? = (25 / 100) × ? = ? / 4

Setting the left-hand side equal to the right-hand side: 55 = ? / 4 ? = 55 × 4 = 220

Explanation

Evaluating the square root terms on the left-hand side: √49 = 7 √196 = 14

Multiplying these square roots together: 7 × 14 = 98

Adding 430 gives the complete value for the left-hand side: 98 + 430 = 528

Now set up the complete equation with the right-hand side: (?)² - 48 = 528

Adding 48 to both sides to isolate (?)²: (?)² = 528 + 48 = 576

Taking the square root of 576: ? = √576 = 24

Explanation

Evaluating each known term in the given equation step-by-step: √484 = 22 (6 / 13) × 260 = 6 × 20 = 120 (17)² = 289

Adding all known numbers on the left-hand side together: 118 + 22 + 120 = 260

Substituting these simplified values back into the main equation: 260 + ? = 289

Subtracting 260 from both sides to determine the missing value ?: ? = 289 - 260 = 29

Explanation

Applying the standard order of operations to the left-hand side expression: First term: 108 ÷ 3 × 5 = 36 × 5 = 180 Second term: 225 ÷ 9 × 4 = 25 × 4 = 100

Subtracting the second term from the first term: 180 - 100 = 80

The right-hand side of the equation is 400% of ?, which simplifies to: (400 / 100) × ? = 4 × ?

Equating the two sides: 80 = 4 × ? ? = 80 / 4 = 20

Explanation

Calculating 40% of 825 on the left-hand side: 40% of 825 = (40 / 100) × 825 = 0.40 × 825 = 330

Converting the percentage on the right-hand side to a fraction: 16 ⅔% = (50 / 3)% = 50 / 300 = 1 / 6

Calculating 1/6 of 1260: (1 / 6) × 1260 = 210

Substituting these evaluated values back into the original equation: 330 = 210 + ?

Subtracting 210 from 330 to isolate ?: ? = 330 - 210 = 120

Explanation

Evaluating each term on the left-hand side of the equation: 18 ÷ 1.5 = 12 153 ÷ 17 = 9 √256 = 16

Adding all three terms on the left-hand side together: 12 + 9 + 16 = 37

Setting the sum equal to the right-hand side expression 629 / ?: 37 = 629 / ?

Multiplying both sides by ? and dividing by 37 to isolate ?: ? = 629 / 37 = 17

Explanation

Evaluating the terms inside the parenthesis on the left-hand side first: √6400 = 80 110 + 70 - 80 = 180 - 80 = 100

Dividing this result by 25 according to the equation: 100 ÷ 25 = 4

Evaluating the right-hand side term: (4)² = 16

Substituting these simplified values into the overall equation: 4 + ? = 16

Subtracting 4 from both sides to find the unknown value ?: ? = 16 - 4 = 12

Explanation

Calculating the numerator expression first: 25% of 680 = (25 / 100) × 680 = (1 / 4) × 680 = 170

Calculating the denominator expression next: 50% of 340 = (50 / 100) × 340 = (1 / 2) × 340 = 170

Substituting the calculated values back into the original fraction equation: ? = (25% of 680) / (50% of 340) ? = 170 / 170 = 1

Explanation

Calculate the left-hand side step by step: 15% of 60 = 9 9 × 36000 = 324000

Set up the equation: 324000 = 12 × ?³ ?³ = 324000 / 12 = 27000 ? = ∛27000 = 30

Explanation

Simplify each fraction: 170 / 34 = 5 25 / 5 = 5 742 / 2226 = 1 / 3

Performing the divisions sequentially from left to right: (5 ÷ 5) ÷ (1 / 3) = 1 ÷ (1 / 3) = 1 × 3 = 3

Explanation

Evaluate the square roots and terms: √441 = 21 √25 = 5

Substitute into the expression: (4 / 10.5) × 21 - 5 = √? 4 × (21 / 10.5) - 5 = √? 4 × 2 - 5 = √? 8 - 5 = 3 = √? ? = 3² = 9

Explanation

Calculate the percentage values on both sides: 12.5% of 400 = (1 / 8) × 400 = 50 60% of 1800 = 0.6 × 1800 = 1080

Substitute into the equation: 50 = ? - 1080 ? = 50 + 1080 = 1130

Explanation

Calculate the square roots: (36)⁽1/2) = √36 = 6 (169)⁽1/2) = √169 = 13

Substitute into the equation: (6 + 13) × ? = 95 19 × ? = 95 ? = 95 / 19 = 5

Explanation

From the given data table, student A attended 136 science workshops, while student C attended 120 economics workshops. To calculate the ratio of science workshops attended by student A to economics workshops attended by student C, we set up the ratio 136 : 120. Dividing both the numerator and denominator by their greatest common divisor of 8 gives 136 / 8 = 17 and 120 / 8 = 15. Hence, the simplified ratio is 17 : 15.

Explanation

From the table, the science workshops attended by students A, B, and C are 136, 134, and 150 respectively. The total sum of science workshops attended by these three students is calculated as 136 + 134 + 150 = 420. The average number of science workshops is obtained by dividing the total sum by the number of students, which yields 420 / 3 = 140.

Explanation

From the given data, student C attended 120 economics workshops and student D attended 80 economics workshops, giving a combined total of 120 + 80 = 200 economics workshops. Student A attended 100 social science workshops. The percentage by which the combined economics workshops exceed A's social science workshops is calculated using the percentage increase formula: [(200 - 100) / 100] × 100 = 100%.

Explanation

Student A attended 188 economics workshops. Since student E attended 25% more economics workshops than student A, the number of economics workshops attended by E is 188 × (1 + 0.25) = 188 × 1.25 = 235. Student B attended 105 social science workshops. The required difference between the economics workshops attended by E and the social science workshops attended by B is 235 - 105 = 130.

Explanation

Student C attended 150 science workshops. Given that the ratio of science workshops to mathematics workshops attended by C is 3 : 1, the number of mathematics workshops attended by C is calculated as 150 / 3 = 50. Student D attended 120 social science workshops. The percentage of C's mathematics workshops relative to D's social science workshops is (50 / 120) × 100 = 500 / 12 = 41.67%.

Explanation

When a train crosses a pole, the distance covered equals the length of the train. Since the distance remains constant, time taken is inversely proportional to speed. The ratio of initial speed to new speed is 72 : (72 + 18) = 72 : 90 = 4 : 5. Consequently, the ratio of initial time to new time is 5 : 4. Since 5 units correspond to the initial time of 25 seconds, 1 unit equals 5 seconds. Therefore, the reduction in time is 1 unit, which equals 5 seconds.

Explanation

To find the net profit percentage, apply the formula for successive percentage changes when an article is marked up and then discounted: Net % = m - d - (m × d) / 100, where m is the markup percentage (40%) and d is the discount percentage (20%). Substituting these values into the formula yields Net % = 40 - 20 - (40 × 20) / 100 = 20 - 8 = 12%.

Explanation

Let the present ages of Dimp and Kajal be 2x and 3x respectively. Dimp's age three years ago was 2x - 3 and Kajal's age five years hence will be 3x + 5. According to the given condition, the sum of these ages equals 52 years, yielding the linear equation (2x - 3) + (3x + 5) = 52. Simplifying gives 5x + 2 = 52, which reduces to 5x = 50, so x = 10. The present age of Dimp is 2x = 2 × 10 = 20.

Explanation

The ratio of profit sharing in a partnership is directly proportional to the ratio of investments made by the partners over equal time periods. Ratio of investments of Tanmay to Ajay = 5600 : 4200 = 4 : 3. Therefore, Tanmay's fraction of the total profit is 4 / (4 + 3) = 4/7. Given that Tanmay's share of the profit is Rs. 8400, the total profit earned by the business is 8400 × (7 / 4) = 14700.

Explanation

The weight of student A is given as 200 kg. Since the weight of C is 20% more than that of A, weight of C = 200 × (1 + 0.20) = 200 × 1.20 = 240 kg. The weight of B is 25% more than that of C, so weight of B = 240 × (1 + 0.25) = 240 × 1.25 = 300 kg. The total sum of the weights of A, B, and C is 200 + 300 + 240 = 740 kg.

Explanation

Let the initial quantities of milk and water be 9x and 5x liters, respectively. When 10 liters of water are added, the new mixture has 9x liters of milk and 5x + 10 liters of water. Setting up the proportion 9x / (5x + 10) = 3 / 5 gives 45x = 15x + 30, which yields 30x = 30 and x = 1. Therefore, the initial quantity of milk is 9 × 1 = 9 liters.

Explanation

Let the breadth of the rectangle be b cm, so its length is b + 8 cm. The perimeter is given by 2(length + breadth) = 2(2b + 8) = 40. Solving 4b + 16 = 40 gives b = 6 cm. Consequently, the length is 14 cm, and the area of the rectangle is 14 × 6 = 84 cm².

Explanation

Simple interest is calculated using SI = (P × R × T) / 100. Substituting the given values gives 2880 = (P × 20 × 6) / 100, which simplifies to 2880 = 1.2P. Solving for P yields P = 2400. Thus, the value of P - 200 is 2400 - 200 = 2200.

Explanation

Let the original number be N. Increasing N by 40% gives 1.4N, and decreasing N by 80% gives 0.2N. The difference between the two results is 1.4N - 0.2N = 1.2N = 360. Dividing 360 by 1.2 gives N = 300.

Explanation

The downstream speed is 24 / 3 = 8 km/hr, and the upstream speed is 24 / 6 = 4 km/hr. The speed of the boat in still water is half the sum of the downstream and upstream speeds: (8 + 4) / 2 = 6 km/hr.

Explanation

Each term in the series is multiplied by 2 to obtain the next term. Starting with 7: 7 × 2 = 14, 14 × 2 = 28, 28 × 2 = 56, 56 × 2 = 112, and 112 × 2 = 224. Therefore, 52 is incorrect and should be replaced by 56.

Explanation

Subtracting 12 from each term gives the successive term in the series: 141 - 12 = 129, 129 - 12 = 117, 117 - 12 = 105, 105 - 12 = 93, 93 - 12 = 81, and 81 - 12 = 69. Thus, 112 is wrong and should be 117.

Explanation

The differences between consecutive terms are 1, 6, 13, 24, 37, and 54, which correspond to second differences of prime numbers: 5, 7, 11, 13, and 17. Adding 17 to 37 gives a final difference of 54, so the last term should be 131 + 54 = 185. Therefore, 186 is incorrect.

Explanation

The differences between consecutive terms are consecutive square numbers starting from 4²: 212 + 4² = 228, 228 + 5² = 253, 253 + 6² = 289, 289 + 7² = 338, 338 + 8² = 402, and 402 + 9² = 483. Thus, 400 is wrong and should be replaced by 402.

Explanation

The series follows the pattern where each term after the first is obtained by multiplying the previous term by an increasing integer and adding 1. Starting from 2: 2 × 1 + 1 = 3, 3 × 2 + 1 = 7, 7 × 3 + 1 = 22, 22 × 4 + 1 = 89, 89 × 5 + 1 = 446, and 446 × 6 + 1 = 2677. Therefore, 6 is wrong and should be replaced by 7.

Explanation

Evaluating each component: ∛729 = 9 37½% = 3/8 5⅓ = 16/3 37½% of 5⅓ = (3/8) × (16/3) = 2

Substituting these values into the equation: 9 + 2 = ? + 2 11 = ? + 2 ? = 9

Explanation

Let the unknown be x. x × 65 ÷ 72 = 195 × 352 ÷ 192

Rearranging to solve for x: x = (195 × 352 × 72) / (192 × 65)

Simplifying the factors: 195 / 65 = 3 72 / 192 = 3 / 8

Substituting back into the equation: x = 3 × 352 × (3 / 8) x = 9 × 44 x = 396

Explanation

Evaluating each quotient separately: 444 ÷ 4 = 111 625 ÷ 25 = 25 2991 ÷ 3 = 997

Summing the results: ? = 111 + 25 + 997 = 1133

Explanation

Evaluating the terms in the equation: √(6.25) = 2.5 5(1/5) = 26/5 7(4/13) = 95/13

Multiplying the fractions: (26/5) × (95/13) = (26/13) × (95/5) = 2 × 19 = 38

Substituting back into the equation: 2.5 + 38 + ? = 72 40.5 + ? = 72 ? = 72 - 40.5 = 31.5

Explanation

Finding the roots: √(7921) = 89 ∛(2197) = 13

Substituting into the expression: ? = (89 - 13) × (1/4) ? = 76 × (1/4) = 19

Explanation

Converting percentages to simple fractions: 266⅔% = 8/3 58⅓% = 7/12

Calculating each term: (8/3) × 153 = 8 × 51 = 408 (7/12) × 300 = 7 × 25 = 175

Summing the values: ? = 408 + 175 = 583

Explanation

Applying BODMAS rules from left to right for multiplication and division: 77077 ÷ 7007 = 11 11 × 125 = 1375 1375 ÷ 5 = 275 275 × 2 = 550

Explanation

Evaluating each percentage term: 25% of 124 = (1/4) × 124 = 31 35% of 60 = (35/100) × 60 = 21

Summing the terms: ? = 31 + 21 = 52

Explanation

Evaluating the left-hand side: 8557 + 1723 = 10280 10280 - 1231 = 9049 9049 - 7321 = 1728

Taking the cube root on both sides: (?³) = 1728 ? = ∛(1728) = 12

Explanation

Simplifying the expression: (?²) = 39 × 1323 × (1/117) (?²) = (39/117) × 1323 (?²) = (1/3) × 1323 (?²) = 441

Taking the square root: ? = √441 = 21