IBPS RRB Clerk Prelims 2022 Numerical Ability Questions with Solutions

Explanation

Lateral surface area of a cylinder is given by LSA = 2 × π × r × h. The net percentage change in the product of two variables increased by a% and b% is given by a + b + (a × b) / 100. Substituting a = 25% and b = 30%:

Net Change = 25 + 30 + (25 × 30) / 100 = 55 + 7.5 = 62.5%

Explanation

The sum of present ages of Mohit and Riya is 60 - 2 × 5 = 50 years. Five years ago, the sum of their ages was 50 - 2 × 5 = 40 years. Given the ratio of Riya's age to Mohit's age five years ago was 3:5, Riya's age five years ago was (3 / 8) × 40 = 15 years. Therefore, Riya's present age is 15 + 5 = 20 years.

Explanation

With interest compounded quarterly, the rate per quarter is r = 40% / 4 = 10%, and nine months equal n = 3 quarters. Total amount A = P × (1 + r / 100)ⁿ = 36000 × (1.1)³ = 36000 × 1.331 = 47916. Compound interest is A - P = 47916 - 36000 = 11916.

Explanation

The sentence states that Priya and Sushma working together can complete the work in days, omitting the required numerical time period. Without this value, x cannot be calculated.

Explanation

Downstream speed is 60 / 2.5 = 24 km/h. Let speed of boat in still water be b and current speed be c. Upstream speed is b - c. Given (b - c) / c = 4 / 1, which gives b = 5c. Downstream speed is b + c = 5c + c = 6c. Setting 6c = 24 gives c = 4 km/h.

Explanation

The relation x% of 3y = y% of 2z simplifies as (x / 100) × 3y = (y / 100) × 2z, which reduces to 3x = 2z or x / z = 2 / 3. Expressing (x + z) / z as (x / z) + 1 yields (2 / 3) + 1 = 5 / 3 = 1⅔.

Explanation

Ram bought 54 bananas for 220. Since 12 bananas make 1 dozen, 54 bananas equal 54 / 12 = 4.5 dozens. The total selling price at 50 per dozen is 4.5 × 50 = 225. Total profit is 225 - 220 = 5.

Explanation

The profit ratio of Pinky to Santosh is (45000 × 9) : (55000 × 12) = 405 : 660 = 27 : 44. Santosh's share of 44 parts corresponds to 8800, so 1 part = 8800 / 44 = 200. Total profit corresponds to 27 + 44 = 71 parts, which equals 71 × 200 = 14200.

Explanation

Let the fraction be n / d. The condition gives (n + 5) / (2d) = 3 / 4, which simplifies to 2n - 3d = -10. Because there are infinitely many pairs of (n, d) satisfying a single linear equation in two variables, the original fraction cannot be uniquely determined.

Explanation

Let the population in 2017 be P. With a 10% annual decrease for 3 years, population in 2020 is P × (1 - 0.10)³ = P × 0.729. Setting P × 0.729 = 14,58,000 gives P = 14,58,000 / 0.729 = 20,00,000, which is 20 lacs.

Explanation

Let the speed of train X be S m/s and its length be L meters. Since train X crosses a pole in 25 seconds, L = 25 × S. The speed of train Y is 90 × (5/18) = 25 m/s, and its length is 400 meters. When running in the same direction, relative speed is (25 - S) m/s. Using the relative speed formula, (400 + 25 × S) / (25 - S) = 180. Solving gives 400 + 25 × S = 4500 - 180 × S, which simplifies to 205 × S = 4100, yielding S = 20 m/s.

Explanation

Evaluating each square root gives √121 = 11, √961 = 31, and √289 = 17. Substituting these values into the expression yields 11 + 31 - 17 = 25. Taking the square root of 25 gives 5.

Explanation

Calculate 20% of 240 = 0.20 × 240 = 48. Calculate 18% of 200 = 0.18 × 200 = 36. Adding the two results together gives 48 + 36 = 84.

Explanation

Cross-multiplying the proportion 121 / ? = ? / 144 gives ?² = 121 × 144. Taking the square root on both sides yields ? = √(121 × 144) = 11 × 12 = 132.

Explanation

First evaluate √625 = 25. Then perform the division 725 ÷ 25 = 29. Next, calculate (2/5) × 600 = 240. Adding these two terms together gives 29 + 240 = 269.

Explanation

Inside the brackets, 1.9 + 2.1 = 4. Multiplying by 12 gives 12 × 4 = 48. Subtracting 12 yields 48 - 12 = 36. Taking the square root gives √36 = 6.

Explanation

Performing the first division gives 2343 ÷ 11 = 213. Performing the second division gives 126 ÷ 3 = 42. Summing these two values gives 213 + 42 = 255.

Explanation

Convert 14(2/7)% to its fractional equivalent 1/7. Calculate (1/7) × 350 = 50. Substituting into the equation gives 50 - (2/3) × ? = 30. Rearranging gives (2/3) × ? = 20, which yields ? = 20 × (3/2) = 30.

Explanation

Simplify the fraction (42 × 12) / (36 × 7) = (42 / 7) × (12 / 36) = 6 × (1/3) = 2. Evaluate √121 = 11. Adding the two results together gives 2 + 11 = 13.

Explanation

First evaluate 10% of 900 = 90, then 20% of 90 = 18. Next, calculate 84 ÷ 12 = 7. Adding the two terms gives 18 + 7 = 25. Taking the square root yields √25 = 5.

Explanation

Applying the order of operations for division, the expression on the left-hand side is evaluated sequentially from left to right. First, calculate 5555 ÷ 11 = 505. Next, divide this result by 5 to obtain 505 ÷ 5 = 101. Equating this to the right-hand side gives 101 = 100 + ?. Subtracting 100 from both sides gives ? = 101 - 100 = 1.

Explanation

Convert all mixed fractions to improper fractions with a common denominator of 6. The left-hand side terms become 2 ⅓ = 7/3 = 14/6, 2 ⅚ = 17/6, and 1 ½ = 3/2 = 9/6. Combining these gives 14/6 + 17/6 - 9/6 = 22/6. The term on the right-hand side is -6 ⅙ = -37/6. Transposing -37/6 to the left-hand side yields ? = 22/6 + 37/6 = 59/6. Converting 59/6 back into a mixed fraction gives 9 ⅚.

Explanation

First, calculate the value of the left-hand side by dividing 1024 by 32, which equals 32. Next, rewrite the mixed fraction on the right-hand side, 2 ½, as an improper fraction 5/2, or decimal 2.5. The equation then becomes 32 = (5/2) × ?. To solve for ?, multiply both sides by the reciprocal 2/5, giving ? = 32 × (2/5) = 64/5 = 12.8.

Explanation

To simplify the expression, perform the additions sequentially from left to right before applying subtraction. Adding the first two terms gives 1231 + 1312 = 2543. Adding the third term yields 2543 + 2113 = 4656. Finally, subtracting the last term gives 4656 - 3211 = 1445. Therefore, the value that replaces the question mark is 1445.

Explanation

Using the identity y² - x² = (y - x)(y + x), substituting the given values yields 72 = 4 × (y + x), which gives y + x = 18. Solving the system of linear equations y + x = 18 and y - x = 4 by addition gives 2y = 22, so y = 11. Subtracting the equations gives 2x = 14, so x = 7. The product x × y = 7 × 11 = 77.

Explanation

Let the length be 7x and the breadth be 3x. The perimeter of a rectangle is 2 × (length + breadth) = 2 × (7x + 3x) = 20x. Given perimeter is 40 cm, so 20x = 40, which gives x = 2. Length = 7 × 2 = 14 cm and breadth = 3 × 2 = 6 cm. Area of rectangle = length × breadth = 14 × 6 = 84 cm².

Explanation

Simple Interest SI = (P × R × T) / 100. Since the principal P = ₹1460 and annual rate R = 10% are identical in both schemes, the difference in interest arises from the difference in duration ΔT = 8 - 5 = 3 years. Difference in interest = (1460 × 10 × 3) / 100 = 1460 × 0.30 = ₹438.

Explanation

Let the cost price of each article be C. The profit on the second article is 0.30 × C and the loss on the first article is 0.18 × C. Net profit = 0.30 × C - 0.18 × C = 0.12 × C. Given net profit is ₹210, so 0.12 × C = 210. C = 210 / 0.12 = 1750. The cost price of each article is ₹1750.

Explanation

The combined cost of purchasing one unit of each article A, B, and C is 52 + 78 + 108 = ₹238. Let n be the equal number of each type of article purchased. Total cost = 238 × n = 1190. n = 1190 / 238 = 5. The man purchased 5 of each type of article.

Explanation

Let the present age of A be 5x years and present age of B be 4x years. Four years hence, age of A = 5x + 4. Six years hence, age of B = 4x + 6. According to the given condition, 5x + 4 = (4x + 6) + 3. Simplifying gives 5x + 4 = 4x + 9, which reduces to x = 5. Present age of B = 4x = 4 × 5 = 20 years.

Explanation

In 120 liters of mixture with milk and water in 5 : 3 ratio: Initial milk = 120 × (5 / 8) = 75 liters. Initial water = 120 × (3 / 8) = 45 liters. Adding 20 liters of milk gives new milk volume = 75 + 20 = 95 liters. Water volume remains 45 liters. Ratio of water to milk in the resulting mixture = 45 : 95 = 9 : 19.

Explanation

Time taken by first car = 5 hours. Time taken by second car = 3 hours 20 minutes = 3 + 20 / 60 = 10 / 3 hours. Ratio of time taken = 5 : (10 / 3) = 15 : 10 = 3 : 2. Since distance covered is identical, speed is inversely proportional to time, making x : y = 2 : 3.

Explanation

Let speed of boat in still water be v km/hr. Stream speed s = 3 km/hr. Upstream speed = v - 3 and downstream speed = v + 3. Since distance = speed × time, equating upstream and downstream distances gives: 5 × (v - 3) = 2 × (v + 3) 5v - 15 = 2v + 6 3v = 21, so v = 7 km/hr. Distance = 5 × (7 - 3) = 20 km.

Explanation

Efficiency ratio of A to B = 140 : 100 = 7 : 5. Since efficiency is inversely proportional to time taken, time ratio of A to B = 5 : 7. Let time taken by A be 5x days and B be 7x days. Given time difference 7x - 5x = 2x = 6 days, so x = 3. Time taken by A alone = 5x = 5 × 3 = 15 days.

Explanation

To find the missing term in the number series, calculate the difference between consecutive terms: 4 - 2 = 2 7 - 4 = 3 12 - 7 = 5 19 - 12 = 7 The differences form a sequence of consecutive prime numbers starting from 2, which are 2, 3, 5, and 7. The next prime number following 7 is 11. Adding this next prime difference of 11 to the preceding term 19 gives the missing number: 19 + 11 = 30.

Explanation

To determine the missing term in the given number series, compute the common difference between successive terms: 98 - 67 = 31 129 - 98 = 31 160 - 129 = 31 This establishes that the series is an arithmetic progression with a constant common difference of 31. Adding 31 to 160 gives the missing value: 160 + 31 = 191. Verifying with the subsequent term, 191 + 31 = 222, confirms the pattern.

Explanation

To solve the number series, examine the differences between adjacent terms: 18 - 10 = 8 = 2³ 45 - 18 = 27 = 3³ 109 - 45 = 64 = 4³ The differences are consecutive perfect cubes starting from 2³. The next term in the pattern requires adding 5³, which equals 125, to 109. Calculating 109 + 125 gives 234. Verifying with the final term, 234 + 6³ = 234 + 216 = 450, confirms that 234 is correct.

Explanation

To find the missing term in the given sequence, evaluate the difference between consecutive terms: 16 - 12 = 4 = 2² 25 - 16 = 9 = 3² 41 - 25 = 16 = 4² The sequence of differences consists of perfect squares of consecutive integers starting from 2². Following this pattern, the next difference must be 5² = 25. Adding 25 to 41 yields 41 + 25 = 66. Verifying the subsequent term gives 66 + 6² = 66 + 36 = 102.

Explanation

To determine the missing number in the sequence, analyze the difference between each pair of consecutive terms: 20 - 15 = 5 25 - 20 = 5 30 - 25 = 5 The given series is an arithmetic progression where each term increases by a fixed constant of 5. Adding 5 to the term 30 yields 30 + 5 = 35. Verifying with the next term, 35 + 5 = 40, confirms that 35 correctly completes the series.

Explanation

To calculate the required percentage excess: Total sunflowers used in January and March = 68 + 96 = 164. Total roses used in January and February = 72 + 88 = 160. The difference between total sunflowers (January and March) and total roses (January and February) is 164 - 160 = 4. Percentage more = [(Total Sunflowers - Total Roses) / Total Roses] × 100 = (4 / 160) × 100 = 2.5%.

Explanation

To find the average number of all three types of flowers used by the company in March, sum the values for sunflowers, lilies, and roses in March and divide by 3: Sunflowers in March = 96 Lilies in March = 80 Roses in March = 118 Total flowers in March = 96 + 80 + 118 = 294. Average = Total Flowers / Number of Flower Types = 294 / 3 = 98.

Explanation

To find the ratio of total roses used in January to total lilies used in January, extract the required values from the provided table: Number of roses used in January = 72 Number of lilies used in January = 84 Ratio = Roses in January : Lilies in January = 72 : 84. Dividing both terms by their greatest common divisor, 12, simplifies the ratio: 72 ÷ 12 = 6 84 ÷ 12 = 7 The simplified ratio is 6 : 7.

Explanation

Total quantity of Walnut and Raisin sold = 50 kg + 90 kg = 140 kg.

Total quantity of Cashew and Pistachio sold = 80 kg + 40 kg = 120 kg.

Required difference = 140 kg - 120 kg = 20 kg.

Explanation

To solve for the unknown variable x in the algebraic equation 510 / x = √324 + √256, compute the principal square roots of the terms on the right-hand side first: √324 = 18 √256 = 16 Substituting these simplified square root values back into the expression gives: 510 / x = 18 + 16 510 / x = 34 Rearranging the equation to solve for x yields x = 510 / 34 = 15.

Explanation

Evaluating the right-hand side of the equation: 5² + 7² + 17² = 25 + 49 + 289 = 363

Substituting this back into the equation: 3 × (?)² = 363 (?)² = 363 ÷ 3 = 121 ? = √121 = 11

Explanation

Calculate the individual percentages on the right side of the equation: 40% of 420 = (40 ÷ 100) × 420 = 168 44% of 200 = (44 ÷ 100) × 200 = 88

Adding these two values gives: 168 + 88 = 256

The equation simplifies to: (?)² = 256

Taking the square root of both sides yields: ? = √256 = 16

Explanation

Convert each mixed fraction into an improper fraction: 2 ⅓ = 7/3 4 2/7 = 30/7 3 ⅓ = 10/3

Now substitute these values into the product: (7/3) × (30/7) × (10/3) × 81

Multiplying the first two terms gives: (7/3) × (30/7) = 10

Next, multiply 10 by the remaining terms: 10 × (10/3) × 81 = (100 ÷ 3) × 81 = 100 × 27 = 2700

Explanation

Evaluate each term step by step: √256 = 16 √49 = 7 16² = 256 ∛343 = 7

Substitute these calculated values back into the expression: (16 × 7) + 256 - 7

Perform multiplication before addition and subtraction: 112 + 256 - 7 = 361

The equation becomes: (?)² = 361

Taking the square root of both sides gives: ? = √361 = 19

Explanation

Calculate each component of the expression on the left side: √256 = 16 √169 = 13 16 × 13 = 208 3600 ÷ 12 = 300

Adding these results gives: 208 + 300 = 508

Set up the simplified equation: 508 = 800 - ?

Subtracting 508 from 800 yields the required answer: ? = 800 - 508 = 292

Explanation

Follow the order of operations to simplify the left side of the equation: 37.5 × 14 = 525 26² = 676

Substitute these values back into the full expression: 525 + 800 - 676 + 136

Perform addition and subtraction from left to right: 525 + 800 = 1325 1325 - 676 = 649 649 + 136 = 785