IBPS RRB Clerk Prelims 2022 Numerical Ability Questions with Solutions

Explanation

Evaluate the square root term: √81 = 9

Add the terms on the left side: 119 + 41 + 9 = 169

Solve for the unknown: ?² = 169 ? = √169 = 13

Explanation

Evaluating the left-hand side using standard order of operations: 1391 ÷ 26 × 2 = (1391 ÷ 26) × 2 = 53.5 × 2 = 107

The equation is 107 = ? - 16². Since 16² = 256, we calculate: ? = 107 + 256 = 363

Explanation

Evaluating each squared term in the sum: 5² = 25 2² = 4

Summing all terms together: 111 + 41 + 25 + 4 = 181

Explanation

Let the unknown value be x, so the equation is 109 times the square root of x, minus (61/21) times x, equals 48 times the square root of x. Moving terms gives 109 root x minus 48 root x equals (61/21) times x, which simplifies to 61 root x equals (61/21) times x. Dividing both sides by 61 gives root x equals x divided by 21, or equivalently 21 root x equals x. Setting t equal to root x turns this into t squared equals 21t, so t equals 21, meaning root x equals 21 and x equals 441. Substituting back, 109 times 21 is 2289, and (61/21) times 441 is 1281, giving 2289 minus 1281 equals 1008, which matches 48 times 21 equals 1008, confirming x equals 441.

Explanation

150% of 20 equals 30. The term 323/17 simplifies to 19. The right side of the equation, 9 squared, equals 81. Subtracting the known terms from the right side gives the square root term: 81 minus 30 minus 19 equals 32, so the square root of the unknown value equals 32. Squaring 32 gives 1024, so the value in place of the question mark is 1024.

Explanation

The given series follows a multiplication pattern with an increment of 0.5 at each step: 60 × 0.5 = 30 30 × 1 = 30 30 × 1.5 = 45 45 × 2 = 90 90 × 2.5 = 225 225 × 3 = 675 Replacing 725 with 675 completes the correct sequence.

Explanation

The differences between consecutive terms in the series follow an arithmetic progression of multiples of 11: 17 + 11 = 28 28 + 22 = 50 50 + 33 = 83 83 + 44 = 127 127 + 55 = 182 182 + 66 = 248 Replacing 29 with 28 establishes the correct term-to-term differences of 11, 22, 33, 44, 55, and 66.

Explanation

Each term in the series is generated by the formula 3ⁿ - 1 for n = 1, 2, 3, 4, 5, 6, 7: 3¹ - 1 = 2 3² - 1 = 8 3³ - 1 = 26 3⁴ - 1 = 80 3⁵ - 1 = 242 3⁶ - 1 = 728 3⁷ - 1 = 2186 The last term should be 2186 instead of 2188.

Explanation

The differences between successive terms increase by 0.6 at each step: 7.7 - 7.1 = 0.6 8.9 - 7.7 = 1.2 10.7 - 8.9 = 1.8 13.1 - 10.7 = 2.4 16.1 - 13.1 = 3.0 The next difference should be 3.6, which gives 16.1 + 3.6 = 19.7 instead of 19.8.

Explanation

The differences between consecutive terms follow the rule n² + 1 for n = 1, 2, 3, 4, 5, 6: 1² + 1 = 2 2² + 1 = 5 3² + 1 = 10 4² + 1 = 17 5² + 1 = 26 6² + 1 = 37 Applying these differences to the terms: 2 + 2 = 4 4 + 5 = 9 9 + 10 = 19 19 + 17 = 36 36 + 26 = 62 62 + 37 = 99 The fourth term should be 19 instead of 18.

Explanation

Total cost price = Purchase price + Repairing cost = 26600 + 1400 = 28000 rupees. Profit percentage = 12.5% = 1/8. Selling price X = Cost price × (1 + 0.125) = 28000 × 1.125 = 31500 rupees.

Explanation

Total cost price of mixture = (24 × 50) + (16 × 40) = 1200 + 640 = 1840 rupees. Total weight = 24 + 16 = 40 kg. Cost price per kg = 1840 / 40 = 46 rupees. To earn 25% profit, selling price per kg = 46 × 1.25 = 57.5 rupees.

Explanation

Let u be the speed of the boat in still water and v be the stream speed in km/hr. Distance difference in 6 hours = 6(u + v) - 6(u - v) = 12v = 24, which gives v = 2 km/hr. Total time for the round trip of 35 km each way is 6 hours: 35 / (u + 2) + 35 / (u - 2) = 6 35 × (2u) / (u² - 4) = 6 70u = 6u² - 24 3u² - 35u - 12 = 0 Solving the quadratic equation gives (3u + 1)(u - 12) = 0. Since speed must be positive, u = 12 km/hr.

Explanation

Total present age of A, B, C, and D = 30 × 4 = 120 years. A's age equals the group average, so A = 30 years. Sum of present ages of B, C, and D = 120 - 30 = 90 years. Using the given relations B = D + 14 and C = D - 2: (D + 14) + (D - 2) + D = 90 3D + 12 = 90 D = 26 years. Present age of C = 26 - 2 = 24 years. Age of C five years ago = 24 - 5 = 19 years.

Explanation

Speed = 4 m/sec. Time = 1 hr 40 min 30 sec = 3600 + 2400 + 30 = 6030 seconds. Distance = Speed × Time = 4 × 6030 = 24120 meters = 24.12 km.

Explanation

Let the share of P be 6x. The share of R is half of P, which gives 3x, and the share of Q is one-third of P, which gives 2x. The sum of all three shares is 6x + 3x + 2x = 11x. Since the total amount distributed is ₹13200, setting 11x = 13200 yields x = 1200. The combined share of Q and R is 2x + 3x = 5x. Substituting x = 1200 into 5x gives 5 × 1200 = ₹6000.

Explanation

A principal doubling in 3 years at simple interest implies that the interest earned in 3 years equals the principal itself, giving an annual interest rate of 100/3% per year. Using the simple interest formula SI = (P × R × T) / 100 for a principal of ₹4200 over 5 years: SI = (4200 × (100/3) × 5) / 100 SI = 4200 × 5 / 3 = 1400 × 5 = ₹7000.

Explanation

Equating the volume of the cuboid to the volume of the cylinder: Length × Breadth × Height = π × r² × h 120 × 88 × 20 = (22/7) × r² × 67200 211200 = (22/7) × 67200 × r² 211200 / 67200 = (22/7) × r² 22/7 = (22/7) × r² r² = 1 r = 1 cm The diameter of the wire is twice the radius, so Diameter = 2 × 1 = 2 cm.

Explanation

The equivalent monthly investment for P is calculated as: 12000 × 8 + (12000 - 2400) × 4 = 96000 + 38400 = 134400. The equivalent monthly investment for Q is calculated as: 9000 × 4 + (9000 - X) × 8 = 36000 + 72000 - 8X = 108000 - 8X. Given the profit ratio of P to Q is 168 : 125, setting up the proportion: 134400 / (108000 - 8X) = 168 / 125 134400 / 168 = 800 800 × 125 = 108000 - 8X 100000 = 108000 - 8X 8X = 8000 X = 1000.

Explanation

Initial total marks for 5 subjects = 5 × 65 = 325. Sum of incorrectly recorded marks = 58 + 68 = 126. Sum of correct marks = 85 + 86 = 171. The net increase in total marks is 171 - 126 = 45. Actual total marks = 325 + 45 = 370. Actual average marks = 370 / 5 = 74.

Explanation

Reducing a number by 25% leaves 75% of its original value. Let N be the original number, so 0.75 × N = 150. Solving for N gives N = 150 / 0.75 = 200. To increase N from 200 to 250, the required increase is 250 - 200 = 50. Percentage increase = (50 / 200) × 100 = 25%.

Explanation

Speed of train A = 54 × (5/18) = 15 m/s. Crossing a platform of 100 meters in 40 seconds means: Length of train A + 100 = 15 × 40 = 600 meters. Length of train A = 500 meters. Speed of train B = 90 × (5/18) = 25 m/s. Relative speed in opposite directions = 15 + 25 = 40 m/s. Total distance to cross train B = 500 + 700 = 1200 meters. Time in seconds = 1200 / 40 = 30 seconds. Converting seconds to minutes gives 30 / 60 = 0.5 minutes, so t = 0.5.

Explanation

A works for 3 days and can complete the entire work alone in 10 days. Fraction of total work done by A = 3 / 10. Total remuneration for the work is ₹6000. Wage share for A = (3 / 10) × 6000 = ₹1800.

Explanation

For store P, ratio of coolers to ACs is 9 : 5 with 216 coolers sold, giving ACs sold by P = 216 × (5 / 9) = 120. For store R, ratio of coolers to ACs is 4 : 1 with 400 coolers sold, giving ACs sold by R = 400 × (1 / 4) = 100. For store S, ratio of coolers to ACs is 3 : 1 with 300 coolers sold, giving ACs sold by S = 300 × (1 / 3) = 100. Total ACs sold by R and S together = 100 + 100 = 200. The ratio of total ACs sold by R and S together to ACs sold by P = 200 : 120 = 5 : 3.

Explanation

For store Q, ratio of coolers to ACs is 6 : 5 with 480 coolers sold, giving ACs sold by Q = 480 × (5 / 6) = 400. For store T, ratio of coolers to ACs is 3 : 2 with 240 coolers sold, giving ACs sold by T = 240 × (2 / 3) = 160. The difference in AC sales between store Q and store T = 400 - 160 = 240. Percentage less = (240 / 400) × 100 = 60%.

Explanation

Number of ACs sold by store Q = 480 × (5 / 6) = 400. Number of coolers sold by store S = 300. Required percentage less = [(400 - 300) / 400] × 100 = (100 / 400) × 100 = 25%.

Explanation

Number of ACs sold by store P = 216 × (5 / 9) = 120. Number of ACs sold by store T = 240 × (2 / 3) = 160. Average number of ACs sold by stores P and T = (120 + 160) / 2 = 140.

Explanation

Number of ACs sold by store Q = 480 × (5 / 6) = 400. Non-defective ACs from store Q = 400 × 0.60 = 240. Number of ACs sold by store R = 400 × (1 / 4) = 100. Non-defective ACs from store R = 100 × 0.80 = 80. Total non-defective ACs sold by both stores = 240 + 80 = 320.

Explanation

Using order of operations: √484 = 22 11² / 8 = 121 / 8 22 ÷ (121 / 8) = 22 × (8 / 121) = 16 / 11 ? = 49 / 11 - 16 / 11 = 33 / 11 = 3.

Explanation

Calculate the fraction part: (5 / 12) × 84 = 35 Calculate the percentage expression: ?% of 3200 = (? × 3200) / 100 = 32 × ? Set up the equation: (32 × ?) ÷ 35 = 64 32 × ? = 64 × 35 ? = (64 × 35) / 32 = 2 × 35 = 70.

Explanation

Evaluating the terms: 32 × 17 = 544 ? = 1156 - 544 = 612.

Explanation

Simplifying the expression using division and multiplication: 96 ÷ 168 = 4 / 7 588 ÷ 12 = 49 ? = (4 / 7) × 49 = 4 × 7 = 28.

Explanation

Convert 11(1/9)% to its fractional equivalent 1/9. (1 / 9) × 873 = 97 Calculate the square root: √2116 = 46 Substitute into the equation: 97 - ? = 46 ? = 97 - 46 = 51.

Explanation

Separate the whole numbers and fractions: Whole number part = 2 + 4 - 3 = 3 Fractional part = 4/7 + 1/3 - 2/3 + 16/21 Convert fractions to a common denominator of 21: 4/7 = 12/21 1/3 = 7/21 2/3 = 14/21 Fractional part = 12/21 + 7/21 - 14/21 + 16/21 = 21/21 = 1 Sum = 3 + 1 = 4.

Explanation

Evaluate 8² = 64. Substitute into the equation: (? × 48) ÷ 54 + 64 = 96 (? × 48) ÷ 54 = 96 - 64 = 32 (? × 48) / 54 = 32 Simplify 48/54 to 8/9: ? × (8 / 9) = 32 ? = (32 × 9) / 8 = 4 × 9 = 36.

Explanation

Applying the standard order of operations (BODMAS/PEMDAS) for addition and subtraction:

First, sum the initial two positive numbers: 4520 + 3560 = 8080

Next, subtract 2680 from this sum: 8080 - 2680 = 5400

Finally, add the remaining term 1680 to get the final result: 5400 + 1680 = 7080

Alternatively, combining all positive terms first gives: (4520 + 3560 + 1680) - 2680 = 9760 - 2680 = 7080

Explanation

According to the BODMAS rule, operations are performed in the order of division, multiplication, addition, and subtraction:

First, evaluate the term involving division and multiplication: (11 ÷ 23) × 6969 = 11 × (6969 ÷ 23) = 11 × 303 = 3333

Second, evaluate the second multiplication term: 55 × 20 = 1100

Third, substitute these computed values back into the given mathematical expression: 3333 + 1100 - 200

Finally, perform the addition and subtraction from left to right: 3333 + 1100 = 4433 4433 - 200 = 4233

Explanation

According to the order of operations, evaluate square roots and multiplications before performing addition and subtraction:

Simplify the square root term using the product property of square roots, √(a × b × c) = √a × √b × √c: √(256 × 81 × 4) = √256 × √81 × √4 = 16 × 9 × 2 = 288

Evaluate the multiplication term: 160 × 2.5 = 400

Substitute the values back into the main expression: 288 - 400 + 400

Perform addition and subtraction from left to right: 288 - 400 = -112 -112 + 400 = 288

Explanation

Using the BODMAS rule, evaluate percentages and multiplications prior to addition and subtraction:

Calculate 250% of 1600: (250 / 100) × 1600 = 2.5 × 1600 = 4000

Evaluate the multiplication of the fraction and integer: 320 × (3 / 8) = (320 / 8) × 3 = 40 × 3 = 120

Substitute these results back into the given expression: 4000 - 120 + 1120

Complete the expression by performing addition and subtraction from left to right: 4000 - 120 = 3880 3880 + 1120 = 5000

Explanation

Following the BODMAS rule, operations inside parentheses are computed first, with division and multiplication taking precedence over addition and subtraction:

Simplify the expression within the parentheses: 3 × 1450 ÷ 2 = (3 × 1450) ÷ 2 = 4350 ÷ 2 = 2175

Substitute this result back into the main expression: 5400 - 2175 + 175

Perform subtraction and addition from left to right: 5400 - 2175 = 3225 3225 + 175 = 3400

Alternatively, regrouping gives: 5400 + 175 - 2175 = 5575 - 2175 = 3400

Explanation

Total number of visitors in Agra Fort on Sunday, Tuesday, and Friday combined: Visitors on Sunday = 600 Visitors on Tuesday = 300 Visitors on Friday = 700 Sum = 600 + 300 + 700 = 1600.

Explanation

Total visitors on Monday for Taj Mahal and Agra Fort combined: 350 + 250 = 600. Total visitors on Saturday for Taj Mahal and Agra Fort combined: 750 + 500 = 1250. Ratio of total visitors on Monday to Saturday = 600 : 1250 = 12 : 25.

Explanation

The visitor count in Taj Mahal on Monday, Thursday, and Friday is 350, 550, and 600 respectively. Average = (350 + 550 + 600) / 3 = 1500 / 3 = 500.

Explanation

Total visitors in Taj Mahal during the week: 350 + 400 + 500 + 550 + 600 + 750 + 800 = 3950. Total visitors in Agra Fort during the week: 250 + 300 + 450 + 200 + 700 + 500 + 600 = 3000. Difference = 3950 - 3000 = 950.

Explanation

The sequence follows an additive pattern where the differences between consecutive terms double at each step: 5 - 3 = 2 9 - 5 = 4 17 - 9 = 8 33 - 17 = 16 The next difference is 16 × 2 = 32. Adding 32 to the last term: 33 + 32 = 65.

Explanation

The sequence increases by consecutive prime numbers: 5 - 3 = 2 8 - 5 = 3 13 - 8 = 5 20 - 13 = 7 The prime number following 7 is 11. Adding 11 to the last term: 20 + 11 = 31.

Explanation

The pattern in the series involves multiplying each term by a factor that is halved at each step: 1 × 16 = 16 16 × 8 = 128 128 × 4 = 512 512 × 2 = 1024 The next multiplier is 2 / 2 = 1. Next term = 1024 × 1 = 1024.

Explanation

The relationship between successive terms in the series follows the formula T(n+1) = T(n) × n + n: 1 × 1 + 1 = 2 2 × 2 + 2 = 6 6 × 3 + 3 = 21 21 × 4 + 4 = 88 For the next term, multiply 88 by 5 and add 5: 88 × 5 + 5 = 440 + 5 = 445.

Explanation

The differences between successive terms are consecutive perfect squares: 6 - 5 = 1 = 1² 10 - 6 = 4 = 2² 19 - 10 = 9 = 3² 35 - 19 = 16 = 4² The next difference is 5² = 25. Adding 25 to 35 yields 35 + 25 = 60.

Explanation

In container A, water content is 100% - 80% = 20%. In container B, water content is given as 60%. The final mixture requires equal water and milk, which corresponds to 50% water content. By the rule of alligation on water percentages: Ratio of mixture A to mixture B = (60 - 50) : (50 - 20) = 10 : 30 = 1 : 3.