IBPS RRB Clerk Prelims 2022 Numerical Ability Questions with Solutions

Explanation

To find the wrong number in the series, evaluate the differences between consecutive terms: 10 - 5 = 5 26 - 10 = 16 50 - 26 = 24 82 - 50 = 32

Examining the second differences, the difference increases by 8 at each step starting from 16 (16, 24, 32). Continuing this constant addition of 8 to find the next differences: Next difference = 32 + 8 = 40 82 + 40 = 122

Subsequent difference = 40 + 8 = 48 122 + 48 = 170

Since 122 correctly completes the sequence up to 170, the number 124 is incorrect.

Explanation

To identify the wrong number, calculate the differences between adjacent terms from right to left: 82 - 54 = 28 106 - 82 = 24 126 - 106 = 20 142 - 126 = 16 154 - 142 = 12

The differences form an arithmetic progression decreasing by 4 at each step: 28, 24, 20, 16, 12. Following this arithmetic sequence, the difference between the first two terms must be: 12 - 4 = 8

Adding 8 to the second term gives: 154 + 8 = 162

Thus, the correct first term is 162, making 160 the wrong number in the series.

Explanation

To determine the wrong number in the series, calculate the difference between consecutive terms: 50 - 65 = -15 80 - 50 = +30 35 - 80 = -45 95 - 35 = +60 20 - 95 = -75

The pattern involves alternating subtraction and addition of increasing multiples of 15: -15, +30, -45, +60, -75, +90. Applying the next step in the pattern to the term 20: 20 + 90 = 110

The sequence requires the last number to be 110 instead of 105, which makes 105 the incorrect value.

Explanation

To calculate the average number of Bollywood movies watched by students A, B, and D, first calculate the individual counts using the total movies and the ratio of Hollywood to Bollywood movies:

Student A: Total = 350, Ratio = 4:3. Bollywood movies = 350 × (3 ÷ 7) = 150

Student B: Total = 400, Ratio = 11:9. Bollywood movies = 400 × (9 ÷ 20) = 180

Student D: Total = 200, Ratio = 13:12. Bollywood movies = 200 × (12 ÷ 25) = 96

Sum of Bollywood movies for A, B, and D = 150 + 180 + 96 = 426 Average = 426 ÷ 3 = 142

Explanation

To find the required ratio, calculate both quantities separately using the given dataset:

Total number of movies watched by student C and student D together: Total = 250 + 200 = 450

Number of Bollywood movies watched by student B, student C, and student E: For student B: 400 × (9 ÷ 20) = 180 For student C: 250 × (7 ÷ 10) = 175 For student E: 375 × (9 ÷ 25) = 135 Sum of Bollywood movies = 180 + 175 + 135 = 490

Ratio of total movies (C | D) to Bollywood movies (B, C | E) = 450 : 490 = 45 : 49

Explanation

To determine the percentage, first find the average total movies watched for both pairs of students:

Average total movies watched by students B and D: (400 + 200) ÷ 2 = 600 ÷ 2 = 300

Average total movies watched by students A and C: (350 + 250) ÷ 2 = 600 ÷ 2 = 300

Calculate the percentage: Percentage = (300 ÷ 300) × 100% = 100%

Explanation

To find the value of the unknown variable x in the equation, simplify the mathematical operations step by step:

Equation: {(400% of x + 15 × 12) - 140} = 60

Step 1: Simplify the percentage and multiplication terms inside the brackets. 400% of x = (400 ÷ 100) × x = 4x 15 × 12 = 180

Step 2: Substitute these values into the original expression. {(4x + 180) - 140} = 60 4x + 40 = 60

Step 3: Solve for x. 4x = 60 - 40 4x = 20 x = 5

Explanation

To solve for the question mark in the given expression, calculate each term using standard order of operations:

Expression: ? = 30% of 1200 - 122 + 7²

Step 1: Evaluate the percentage of the number. 30% of 1200 = (30 ÷ 100) × 1200 = 360

Step 2: Calculate the square term. 7² = 49

Step 3: Substitute the calculated values into the expression and solve. ? = 360 - 122 + 49 ? = 238 + 49 ? = 287

Explanation

22(2/9)% can be converted to the simple fraction 2/9. 2/9 × 72 = 16 √1444 = 38 ? = 16 + 38 = 54

Explanation

25% of 2560 = 2560 / 4 = 640 840 = 640 + 12.5% of ? 200 = 12.5% of ? Since 12.5% = 1/8: ? = 200 × 8 = 1600

Explanation

4! = 4 × 3 × 2 × 1 = 24 20% of 45% of 200 = 0.20 × 0.45 × 200 = 18 ? = 24 + 18 = 42

Explanation

(820 / 510) × (1700 / 410) = ? / 3 (820 / 410) × (1700 / 510) = ? / 3 2 × (10 / 3) = ? / 3 20 / 3 = ? / 3 ? = 20

Explanation

Express all terms in base 8: 8¹⁶ × (8²)³⁵ ÷ (8³)¹² = (8²)^? 8¹⁶ × 8⁷⁰ ÷ 8³⁶ = 8⁽2?) 8⁽16 + 70 - 36) = 8⁽2?) 8⁵⁰ = 8⁽2?) 2? = 50 ? = 25

Explanation

55 × 44 = 2420 17.5% of 1600 = (35 / 2)% × 1600 = 35 × 8 = 280 ? = 2420 + 280 = 2700

Explanation

3½ = 7/2 5¼ = 21/4 1⁴/₉ = 14/9 Setting up the equation: (7/2) × ? ÷ (21/4) = 14/9 (7/2) × ? × (4/21) = 14/9 (2/3) × ? = 14/9 ? = (14/9) × (3/2) = 7/3

Explanation

29² = 841 13 × 3 = 39 29² + 13 × 3 = 841 + 39 = 880 880 = ? × 10 ? = 880 / 10 = 88

Explanation

18² = 324 11² = 121 7³ = 343 ? = 324 - 121 + 343 = 203 + 343 = 546

Explanation

65% of 180 = (65 / 100) × 180 = 117 √841 = 29 15 × √841 = 15 × 29 = 435 ? = 117 + 435 = 552

Explanation

23² = 529 and (4/7) × 168 = 96. Substituting these values into the right-hand side gives 529 - 96 = 433. The equation becomes ?² + 12² = 433, which simplifies to ?² + 144 = 433. Subtracting 144 from 433 gives ?² = 289. Taking the square root gives ? = 17.

Explanation

Simplifying the left-hand side: (45/270) × (162/9) = (1/6) × 18 = 3. Setting up the full equation: 3 = ? + 15. Subtracting 15 from both sides yields ? = -12.

Explanation

Neeraj invested Rs. 7500 for 12 months, while Prashant invested Rs. 8500 (7500 + 1000) for 8 months (12 - 4). The ratio of their profit shares is (7500 × 12) : (8500 × 8) = 90000 : 68000 = 45 : 34. Since Neeraj's share of 45 units equals Rs. 900, 1 unit equals Rs. 20. The total profit corresponds to (45 + 34) = 79 units. Total profit = 79 × 20 = Rs. 1580.

Explanation

The problem states that Vodafone users comprise 30% of the total network users in village T, but no numerical value or relationship is provided to determine the total number of users. Without the total number of users or user counts for Airtel and Jio, it is mathematically impossible to calculate the exact number of Vodafone users.

Explanation

Marked Price = Selling Price ÷ (1 - Discount%) = 450 ÷ 0.75 = Rs 600. Percentage by which Marked Price exceeds Cost Price = [(Marked Price - Cost Price) ÷ Cost Price] × 100. Substituting the values: [(600 - 320) ÷ 320] × 100 = (280 ÷ 320) × 100 = 87.5%.

Explanation

Let the original number be 10x + y, where x is the tens digit and y is the units digit. Given x + y = 11 and (10y + x) - (10x + y) = 45, which simplifies to 9(y - x) = 45, giving y - x = 5. Solving the two linear equations x + y = 11 and y - x = 5 yields y = 8 and x = 3. The original number is 10(3) + 8 = 38.

Explanation

Let the total time taken by Pipe A and Pipe B alone be 3t and 2t hours respectively. The work equation for filling the tank completely is 6 ÷ (3t) + 12 ÷ (2t) = 1, which simplifies to 2/t + 6/t = 1. Solving 8/t = 1 gives t = 8. The time taken by Pipe B alone to fill the tank completely is 2t = 2 × 8 = 16 hours.

Explanation

Let the present ages of P and Q be 6x and 5x respectively. Since R is 8 years younger than Q, R = 5x - 8. Using P + R = 58 gives 6x + (5x - 8) = 58, which simplifies to 11x = 66, so x = 6. The present age of Q is 5 × 6 = 30 years, so six years hence Q's age will be 30 + 6 = 36 years.

Explanation

Let the speed of the stream be v km/hr. Downstream distance is 2 × (15 + v) and upstream distance is 4 × (15 - v). Since downstream distance is 25% less than upstream distance, 2 × (15 + v) = 0.75 × 4 × (15 - v). Simplifying yields 30 + 2v = 45 - 3v, which reduces to 5v = 15, giving v = 3 km/hr.

Explanation

Compound interest earned on Rs 6000 at 10% p.a. for 2 years = 6000 × [(1 + 0.10)² - 1] = 6000 × 0.21 = Rs 1260. Simple interest SI = (P × R × T) ÷ 100. Equating simple interest to 1260 gives 1260 = (10500 × 3 × T) ÷ 100 = 315 × T. Solving for T gives T = 1260 ÷ 315 = 4 years.

Explanation

Investment ratio of A to B is 7:9. A invests for 11 months (7 + 4 months) and B invests for 7 months. Profit ratio A : B = (7 × 11) : (9 × 7) = 77 : 63 = 11 : 9. B's share of the total profit = [9 ÷ (11 + 9)] × 6150 = (9 ÷ 20) × 6150 = Rs 2767.5.

Explanation

Let the length of the platform be L meters. Speed of train A is (240 + L) ÷ 18 m/s and speed of train B is (210 + L) ÷ 24 m/s. Using the speed ratio 3:2 gives [(240 + L) ÷ 18] ÷ [(210 + L) ÷ 24] = 3 ÷ 2. Simplifying yields 4(240 + L) ÷ [3(210 + L)] = 3 ÷ 2, which cross-multiplies to 8(240 + L) = 9(210 + L). Solving 1920 + 8L = 1890 + 9L gives L = 30 meters.

Explanation

The remaining quantity of pure milk after repeated replacements is given by Final Milk = V × (1 - x ÷ V)ⁿ. Substituting initial volume V = 42 liters, replaced volume x = 7 liters, and n = 2 operations: Final Milk = 42 × (1 - 7 ÷ 42)² = 42 × (5 ÷ 6)² = 42 × (25 ÷ 36) = 175 ÷ 6 = 29 ⅙ liters.

Explanation

The radius of a circle with circumference C is given by r = C / (2π). For the circle with circumference 88 m: r₁ = (88 × 7) / (2 × 22) = 14 m. For the circle with circumference 132 m: r₂ = (132 × 7) / (2 × 22) = 21 m. The difference between the areas of the two circles is: ΔA = π × (r₂² - r₁²) ΔA = (22 / 7) × (21² - 14²) = (22 / 7) × (441 - 196) = (22 / 7) × 245 = 22 × 35 = 770 m².

Explanation

To find the number of digital watches sold by each shopkeeper, multiply the total watches sold by the fraction representing digital watches in the given ratio: For shopkeeper A: 1200 × (7 / 16) = 525 For shopkeeper B: 1440 × (7 / 12) = 840 For shopkeeper C: 1650 × (5 / 11) = 750 For shopkeeper D: 1540 × (4 / 7) = 880 For shopkeeper E: 1360 × (13 / 20) = 884 Comparing the totals, shopkeeper E sold the maximum number of digital watches.

Explanation

Analog watches sold by shopkeeper D = 1540 × (3 / 7) = 660. Digital watches sold by shopkeeper C = 1650 × (5 / 11) = 750. The required percentage difference is: Percentage = ((750 - 660) / 750) × 100 = (90 / 750) × 100 = 12%.

Explanation

Total analog watches sold = 1200 × (9 / 16) + 1440 × (5 / 12) + 1650 × (6 / 11) + 1540 × (3 / 7) + 1360 × (7 / 20) Total analog watches = 675 + 600 + 900 + 660 + 476 = 3311. Total digital watches sold = 1200 × (7 / 16) + 1440 × (7 / 12) + 1650 × (5 / 11) + 1540 × (4 / 7) + 1360 × (13 / 20) Total digital watches = 525 + 840 + 750 + 880 + 884 = 3879. Difference between total digital and total analog watches sold = 3879 - 3311 = 568.

Explanation

The given series alternates between adding and subtracting consecutive integers: 24 + 6 = 30 30 - 7 = 23 23 + 8 = 31 31 - 9 = 22 22 + 10 = 32

Explanation

The pattern in the series follows the rule xₙ₊₁ = xₙ × n + n for n starting from 1: 6 × 1 + 1 = 7 7 × 2 + 2 = 16 16 × 3 + 3 = 51 51 × 4 + 4 = 208 208 × 5 + 5 = 1045

Explanation

The pattern involves successive division by consecutive decreasing integers starting from 6: 39600 ÷ 6 = 6600 6600 ÷ 5 = 1320 1320 ÷ 4 = 330 330 ÷ 3 = 110 110 ÷ 2 = 55 The missing number in the sequence is 1320.

Explanation

The pattern adds alternating perfect squares and cubes of consecutive natural numbers: 9 + 1² = 10 10 + 2³ = 18 18 + 3² = 27 27 + 4³ = 91 91 + 5² = 116

Explanation

The differences between consecutive terms decrease by 1 moving forward in the sequence: 454 + 107 = 561 561 + 108 = 669 669 + 109 = 778 778 + 110 = 888 888 + 111 = 999 The missing number is 888.

Explanation

Ankush saves 40% of his salary, which means he spends 60% of his monthly income. 60% of Ankush's income = Rs 28000 Ankush's income = (28000 × 100) / 60 = Rs 140000 / 3 Ankush's income is 77(7/9)% of Aman's income. Expressing 77(7/9)% as a fraction yields 7/9: (7 / 9) × Aman's income = 140000 / 3 Aman's income = (140000 / 3) × (9 / 7) = Rs 60000

Explanation

Let the present ages of A and B be 3x and 2x respectively. According to the given ratio: (3x - 5) / (2x + 10) = 1 / 2 2 × (3x - 5) = 2x + 10 6x - 10 = 2x + 10 4x = 20 x = 5

Sum of present ages of A and B = 3x + 2x = 5x = 5 × 5 = 25 years.

Explanation

Convert division operations into multiplication by multiplying by the reciprocal: (27 / 40) ÷ (1 / 5) × (8 / 9) ÷ (3 / 100) = (27 / 40) × (5 / 1) × (8 / 9) × (100 / 3)

Simplifying step-by-step: (27 / 40) × 5 = 27 / 8 (27 / 8) × (8 / 9) = 3 3 × (100 / 3) = 100

Explanation

Evaluate the expression step-by-step using order of operations: 51% of (1200 / 17) = (51 / 100) × (1200 / 17) = (51 / 17) × (1200 / 100) = 3 × 12 = 36 18² = 324

Adding these terms: 36 + 324 = 360

Now solve for the unknown: 360 = ? × 24 ? = 360 / 24 = 15

Explanation

Evaluate the 'of' expressions first according to BODMAS rules: 25% of 4 = (25 / 100) × 4 = 1 17 of 1 = 17

Substitute back into the expression and solve from left to right: 102² ÷ 17 ÷ 36 = 10404 ÷ 17 ÷ 36 = 612 ÷ 36 = 17

Explanation

Calculate successive percentages of the given number: 35% of 30% of 50% of 6000 = (35 / 100) × (30 / 100) × (50 / 100) × 6000 = 0.35 × 0.30 × 0.50 × 6000 = 0.35 × 0.30 × 3000 = 0.35 × 900 = 315

Explanation

Applying BODMAS rules, perform operations of equal precedence from left to right: 5 × 12 ÷ 8 × 4 = (5 × 12) ÷ 8 × 4 = 60 ÷ 8 × 4 = 7.5 × 4 = 30

Explanation

Evaluate the radical terms: √144 = 12 ∜256 = 4 √324 = 18

Substitute these values into the equation: 12 + 4 + ? = 18 16 + ? = 18 ? = 18 - 16 = 2

Explanation

Apply BODMAS to evaluate division and square root: 24 ÷ 6 = 4 √169 = 13

Substitute these into the equation: 17 + 4 = ? + 13 21 = ? + 13 ? = 21 - 13 = 8

Explanation

Evaluate the squares inside the parentheses: 16² = 256 10² = 100 16² + 10² = 256 + 100 = 356

Apply division by 2/3 and solve for the unknown: 356 ÷ (2 / 3) = 356 × (3 / 2) = 534 534 = ? × 6 ? = 534 / 6 = 89