IBPS RRB Clerk Prelims 2022 Numerical Ability Questions with Solutions

Explanation

The terms in the series follow the alternate square offset rule starting from n = 2: 2² + 1 = 5 3² - 1 = 8 4² + 1 = 17 5² - 1 = 24 6² + 1 = 37 7² - 1 = 48 8² + 1 = 65

Using 37 gives the correct value for 6² + 1.

Explanation

The numbers are obtained by alternating multiplication and division operations using successive even numbers starting with 2: 32 × 2 = 64 64 ÷ 4 = 16 16 × 6 = 96 96 ÷ 8 = 12 12 × 10 = 120 120 ÷ 12 = 10

Applying 120 ÷ 12 yields 10 as the final term.

Explanation

Calculating the differences between successive terms reveals a sequence of consecutive prime numbers starting from 3: 21 - 18 = 3 26 - 21 = 5 33 - 26 = 7 44 - 33 = 11 57 - 44 = 13 74 - 57 = 17

Starting the sequence with 18 produces the prime differences 3, 5, 7, 11, 13, and 17 throughout the series.

Explanation

Wireless mice sold by shopkeeper D = (5 / 8) × 480 = 300. Wired mice sold by shopkeeper C = (2 / 5) × 750 = 300. Percentage = (Wireless mice sold by D / Wired mice sold by C) × 100 = (300 / 300) × 100 = 100%.

Explanation

Wired mice sold by shopkeeper A = (9 / 14) × 840 = 540. Wired mice sold by shopkeeper B = (7 / 13) × 650 = 350. Average number of wired mice sold by A and B = (540 + 350) / 2 = 890 / 2 = 445. Total mice sold by shopkeeper D = 480. Difference = |480 - 445| = 35.

Explanation

Wireless mice sold by shopkeeper B = (6 / 13) × 650 = 300. Wired mice sold by shopkeeper E = (7 / 11) × 550 = 350. Ratio = Wireless mice sold by B : Wired mice sold by E = 300 : 350 = 6 : 7.

Explanation

Total mice sold by shopkeeper B and E together = 650 + 550 = 1200. Total mice sold by shopkeeper C = 750. Percentage difference = [(1200 - 750) / 750] × 100 = (450 / 750) × 100 = 60%.

Explanation

Total mice sold by shopkeeper B = 650. Total mice sold by shopkeeper X = 650 × 1.20 = 780. Ratio of wired to wireless mice sold by X = 23 : 29. Total parts = 23 + 29 = 52 parts. Difference in ratio parts = 29 - 23 = 6 parts. Difference in quantity = (6 / 52) × 780 = 90.

Explanation

Initial volume of mixture = 160 L with water to milk ratio 3 : 7. Initial water = (3 / 10) × 160 = 48 L. Initial milk = (7 / 10) × 160 = 112 L. When 10 L of mixture is removed: Water removed = (3 / 10) × 10 = 3 L. Milk removed = (7 / 10) × 10 = 7 L. Remaining water = 48 - 3 = 45 L. Remaining milk = 112 - 7 = 105 L. After adding 20 L of water, final water = 45 + 20 = 65 L. Final ratio of water to milk = 65 : 105 = 13 : 21.

Explanation

Time taken by Rahul and Ayush together T = (12 × 20) / (12 + 20) = 240 / 32 = 7.5 days. Deepak takes 2.5 days more than their combined time. Time taken by Deepak = 7.5 + 2.5 = 10 days.

Explanation

Area of a circle formula: A = πr². Given area A = 124.74 cm². (22 / 7) × r² = 124.74 r² = (124.74 × 7) / 22 = 39.69 r = √39.69 = 6.3 cm.

Explanation

Let total voters be 100x. Voters who cast their vote = 85x. Invalid votes = 20% of 85x = 17x. Valid votes = 85x - 17x = 68x. Winning candidate gets 50% of total voters = 50x. Losing candidate gets = 68x - 50x = 18x. Margin of victory = 50x - 18x = 32x. Given margin = 3200 votes. 32x = 3200 → x = 100. Total voters = 100 × 100 = 10000.

Explanation

Selling price of article A = ₹1050 at a loss of 6.25% (fraction 1/16). Cost price of article A = 1050 / (1 - 1/16) = 1050 × (16 / 15) = ₹1120. Selling price of article B = ₹1050 at a profit of 16.67% (fraction 1/6). Cost price of article B = 1050 / (1 + 1/6) = 1050 × (6 / 7) = ₹900. Sum of cost prices = 1120 + 900 = ₹2020.

Explanation

Let the ages of Pankaj and Pradeep 5 years ago be 4x and 7x. Their present ages are 4x + 5 and 7x + 5. After 2 years, their ages become 4x + 7 and 7x + 7. According to the problem: (4x + 7) / (7x + 7) = 5 / 8 Cross-multiplying gives: 8(4x + 7) = 5(7x + 7) 32x + 56 = 35x + 35 3x = 21 x = 7 Pradeep's present age = 7x + 5 = 7(7) + 5 = 54 years.

Explanation

Profit share ratio = Investment of Harsh × Time of Harsh : Investment of Veer × Time of Veer Profit ratio = (2500 × 7) : (4000 × 5) = 17500 : 20000 = 7 : 8. Given Harsh's profit share corresponding to 7 parts is Rs. 350. Value per part = 350 / 7 = Rs. 50. Veer's profit share corresponding to 8 parts = 8 × 50 = Rs. 400.

Explanation

Simple Interest formula: SI = (P × R × T) / 100. Interest from Scheme A = (X × 12.5 × 4) / 100 = 0.50X. Interest from Scheme B = (X × 16 × 3) / 100 = 0.48X. Difference between interests = 0.50X - 0.48X = 0.02X. Given 0.02X = 122. X = 122 / 0.02 = 6100.

Explanation

Weighted average = (Sum of marks of girls + Sum of marks of boys) / Total number of students. Total marks of girls = 15 × 54 = 810. Total marks of boys = 25 × 42 = 1050. Total class marks = 810 + 1050 = 1860. Total number of students = 15 + 25 = 40. Average marks of class = 1860 / 40 = 46.5.

Explanation

Let the distance between office and platform be D km. Total time taken = D / 12 + D / 10 = 5.5 hours. (5D + 6D) / 60 = 11 / 2 11D / 60 = 11 / 2 D / 60 = 1 / 2 D = 30 km.

Explanation

The difference pattern between consecutive terms is: 41 - 11 = 30 30 + 22 = 52 52 - 33 = 19 19 + 44 = 63 63 - 55 = 8 Hence, the missing number replacing the question mark is 8.

Explanation

The difference between consecutive terms increases by 2 each step: 47 - 16 = 31 80 - 47 = 33 115 - 80 = 35 152 - 115 = 37 The next difference is 37 + 2 = 39. Missing term = 152 + 39 = 191.

Explanation

The pattern moving left to right multiplying by consecutive numbers is: ? × 1 = 10 ⇒ ? = 10 10 × 2 = 20 20 × 3 = 60 60 × 4 = 240 240 × 5 = 1200 Thus, the value of ? is 10.

Explanation

The differences between successive terms are multiples of 13: 21 - 8 = 13 (13 × 1) 47 - 21 = 26 (13 × 2) 86 - 47 = 39 (13 × 3) 138 - 86 = 52 (13 × 4) 203 - 138 = 65 (13 × 5) The next difference is 13 × 6 = 78. Missing term = 203 + 78 = 281.

Explanation

The difference pattern between consecutive terms is: 12 - 11 = 1 = 1³ 16 - 12 = 4 = 2² 43 - 16 = 27 = 3³ 59 - 43 = 16 = 4² The next difference is 5³ = 125. Missing term = 59 + 125 = 184.

Explanation

To simplify the expression 42 × (22/7) + 20% of 530 - 26, apply the standard order of operations. First, simplify the multiplication with fraction: 42 × (22/7) = (42 ÷ 7) × 22 = 6 × 22 = 132. Second, calculate the percentage term: 20% of 530 = (20/100) × 530 = 0.2 × 530 = 106. Third, substitute these computed values back into the equation: 132 + 106 - 26. Finally, perform addition and subtraction from left to right: 132 + 106 = 238, and 238 - 26 = 212.

Explanation

To find the unknown value in (23 × 23) + 21 × 7 = ?², simplify the left side using basic arithmetic operations. First, compute the square of 23: 23 × 23 = 529. Second, calculate the product of 21 and 7: 21 × 7 = 147. Next, sum these two results: 529 + 147 = 676. Now the equation becomes ?² = 676. Taking the square root on both sides gives ? = √676 = 26.

Explanation

To solve √1444 ÷ 19 + 3.5 × √16 = ?, evaluate the square roots first. The square root of 1444 is 38 because 38 × 38 = 1444. The square root of 16 is 4 because 4 × 4 = 16. Substitute these values back into the given expression: 38 ÷ 19 + 3.5 × 4. Perform division and multiplication from left to right: 38 ÷ 19 = 2 3.5 × 4 = 14 Finally, add the results together: 2 + 14 = 16.

Explanation

To evaluate 780 ÷ 48 × 16 = ?, apply the standard order of operations or simplify the expression using fractional form. Write the expression as (780 × 16) / 48. Simplify the fraction by dividing the numerator and denominator by 16: 48 ÷ 16 = 3. The expression simplifies to 780 / 3. Performing the division gives 780 ÷ 3 = 260.

Explanation

To solve 1486 + 212 - 1704 = ? - (11)², simplify both sides step by step. First, calculate the left side of the equation: 1486 + 212 = 1698 1698 - 1704 = -6 Next, evaluate the exponent on the right side: (11)² = 121. Substitute these values into the equation: -6 = ? - 121 Isolate ? by adding 121 to both sides: ? = 121 - 6 = 115.

Explanation

To solve ? × (8² + 26) = 60², simplify the expressions inside the parentheses and the exponent first. Calculate 8² = 64, so 8² + 26 = 64 + 26 = 90. Calculate 60² = 3600. Substitute these values back into the equation: ? × 90 = 3600 Isolate ? by dividing 3600 by 90: ? = 3600 ÷ 90 = 40.

Explanation

To find the value of ? in ?% of 800 + 8³ = 1024, simplify the exponent first. Calculate 8³ = 8 × 8 × 8 = 512. Substitute this into the equation: ?% of 800 + 512 = 1024 Subtract 512 from both sides to isolate the percentage term: ?% of 800 = 1024 - 512 = 512 Express ?% as (? / 100): (? / 100) × 800 = 512 8 × ? = 512 Divide both sides by 8: ? = 512 ÷ 8 = 64.

Explanation

To solve 281 + ? = 32% of 1700, calculate the percentage on the right side first. 32% of 1700 = (32 / 100) × 1700 = 32 × 17. Calculate 32 × 17 = 544. Substitute this back into the original equation: 281 + ? = 544 Subtract 281 from both sides to isolate ?: ? = 544 - 281 = 263.

Explanation

To evaluate 2⅓ + 3⅙ = ? - 1½, isolate ? by moving -1½ to the left side of the equation: ? = 2⅓ + 3⅙ + 1½. Separate the whole numbers and the fractions: Whole numbers: 2 + 3 + 1 = 6. Fractions: ⅓ + ⅙ + ½. Find a common denominator, which is 6: ⅓ = 2/6, ⅙ = 1/6, ½ = 3/6. Sum of fractions = 2/6 + 1/6 + 3/6 = 6/6 = 1. Combine the whole numbers and fractional sum: ? = 6 + 1 = 7.

Explanation

To find ? in 20% of (? + 96) = 30 × 1.6, simplify the right side of the equation first. Calculate 30 × 1.6 = 48. Express 20% as a fraction: 20% = 20/100 = 1/5. Substitute these into the equation: (1/5) × (? + 96) = 48 Multiply both sides by 5: ? + 96 = 48 × 5 = 240 Subtract 96 from both sides to solve for ?: ? = 240 - 96 = 144.

Explanation

Calculate 48% of 250 using the identity 48% of 250 = 24% of 500 = 120. Substitute this value back into the given percentage expression: 24% of ? + 120 = 240. Subtracting 120 from both sides gives 24% of ? = 120. Expressing 24% as 24/100, the equation becomes (24/100) × ? = 120. Solving for the unknown yields ? = (120 × 100) / 24 = 5 × 100 = 500.

Explanation

Calculate the right-hand side of the equation: 40% of 420 = 0.40 × 420 = 168. Evaluate the square term on the left-hand side: 12² = 144. Set up the simplified equation with the unknown divisor x in place of the expression: (288 / x) + 144 = 168. Subtract 144 from both sides to isolate the fraction term: 288 / x = 168 - 144 = 24. Solve for x by dividing 288 by 24: x = 288 / 24 = 12.

Explanation

Evaluate the multiplication term on the left side: 17.5 × 8 = (35 / 2) × 8 = 140. Evaluate the numerical terms on the right side: 20² + 100 = 400 + 100 = 500. Substitute these simplified values back into the original equation: 140 + ? = 500. Subtract 140 from both sides to determine the unknown value: ? = 500 - 140 = 360.

Explanation

Calculate 25% of 960 by dividing 960 by 4, which yields 960 / 4 = 240. Calculate the product of the second term: 24 × 15 = 24 × (10 + 5) = 240 + 120 = 360. Substitute both evaluated values into the expression to solve for the missing question mark: ? = 240 + 360 = 600.

Explanation

Evaluate the term on the right-hand side of the equation: 29.2 × 20 = 584. Evaluate the square term on the left-hand side: 24² = 576. The expression simplifies to ³√? + 576 = 584. Subtract 576 from both sides to isolate the cube root of the unknown number: ³√? = 584 - 576 = 8. Cube both sides of the equation to find the value of the unknown: ? = 8³ = 512.

Explanation

Total work = 20 × 22 = 440 man-days. Work completed in the first 10 days = 20 × 10 = 200 man-days. Remaining work = 440 - 200 = 240 man-days. The total time taken is 6 days less than projected, which is 22 - 6 = 16 days. Thus, the remaining time available is 16 - 10 = 6 days. Let the new team size be (20 + X). (20 + X) × 6 = 240 20 + X = 40 X = 20.

Explanation

In the 440 ml mixture: Water = 40% of 440 = 176 ml. Milk = 440 - 176 = 264 ml. After adding 54 ml of water and 66 ml of milk: New water quantity = 176 + 54 = 230 ml. New milk quantity = 264 + 66 = 330 ml. Ratio of milk to water = 330 : 230 = 33 : 23.

Explanation

Let the number of yellow balls be Y. Total balls = 5 + 7 + Y = 12 + Y. Given probability of choosing a yellow ball = Y / (12 + Y) = 2/5. 5Y = 2(12 + Y) 5Y = 24 + 2Y 3Y = 24 Y = 8. Total balls = 12 + 8 = 20.

Explanation

Upstream speed = 120 km / 10 hours = 12 km/h. Downstream speed = 12 × (1 + 66.67%) = 12 × (1 + 2/3) = 20 km/h. Speed of stream = (Downstream speed - Upstream speed) / 2 = (20 - 12) / 2 = 4 km/h.

Explanation

Let total tank capacity = LCM(15, 18) = 90 units. Efficiency of pipe A = 90 / 15 = 6 units/hour. Efficiency of pipe B = 90 / 18 = 5 units/hour. Work completed in the first 5 hours by both pipes = (6 + 5) × 5 = 55 units. Remaining work = 90 - 55 = 35 units. Time taken by pipe B alone to finish the remaining work = 35 / 5 = 7 hours. Total time taken = 5 + 7 = 12 hours.

Explanation

Total ratio parts = 7 + 11 + 5 = 23 parts. Value of 1 part = 690 / 23 = 30 toffees. Difference between Jyoti's and Sagar's share = 7 - 5 = 2 parts. Difference in toffees = 2 × 30 = 60.

Explanation

Side of the square = 56 / 4 = 14 m. Area of the square = 14² = 196 m². Area of the rectangle = 196 - 100 = 96 m². Breadth of the rectangle = 96 / 12 = 8 m. Ratio of length to breadth = 12 : 8 = 3 : 2.

Explanation

Sum of weights of the three persons = 51 × 3 = 153 kg. Let the weight of the second person be W. Weight of the first person = W + 14. Weight of the third person = W - 5. (W + 14) + W + (W - 5) = 153 3W + 9 = 153 3W = 144 W = 48 kg. Weight of the first person = 48 + 14 = 62 kg.

Explanation

Rate of interest per half-year r = 20% / 2 = 10%. Number of half-year periods n = 1.5 × 2 = 3. Effective compound interest rate = (1 + 0.10)³ - 1 = 1.331 - 1 = 0.331 or 33.1%. Principal = Interest / Effective rate = 1986 / 0.331 = Rs. 6000.

Explanation

Let the total monthly income be 100%. Expenditure on food = 30%. Savings = 20%. Difference between food expenditure and savings = 30% - 20% = 10%. Given 10% of income = Rs. 1800. Expenditure on rent = 25% of income = (1800 / 10) × 25 = Rs. 4500.

Explanation

To identify the wrong term in the given number series, observe the mathematical pattern relating consecutive numbers. The series follows an alternating sequence of two operations: multiplying by 6 and dividing by 8. 64 × 6 = 384 384 ÷ 8 = 48 48 × 6 = 288 288 ÷ 8 = 36 36 × 6 = 216 216 ÷ 8 = 27

Following this consistent pattern, the final term should be 27 instead of 28. Therefore, 28 is the wrong number in the given series.

Explanation

To find the wrong number in the series, analyze the pattern relating each term to the next. The sequence follows a rule where each term is multiplied by consecutive integers starting from 1, and the same integer is added to the product: T(n+1) = T(n) × n + n. Starting with 14 as the first term: 14 × 1 + 1 = 15 15 × 2 + 2 = 32 32 × 3 + 3 = 99 99 × 4 + 4 = 400 400 × 5 + 5 = 2005 2005 × 6 + 6 = 12036

Every term after the first matches the pattern perfectly when starting from 14. Therefore, 16 is the wrong term in the given series.