IBPS RRB Clerk Prelims 2025 Numerical Ability Questions with Solutions

Explanation

To find the unknown value represented by the question mark, simplify the square root of 3025. Since 50² = 2500 and 60² = 3600, 3025 ends in 25, which gives √3025 = 55. Substituting 55 into the original equation: √x × 55 = 2695 Isolate √x by dividing both sides of the equation by 55: √x = 2695 ÷ 55 2695 ÷ 55 = 49 To obtain x, square both sides: x = 49² = (50 - 1)² = 2500 - 100 + 1 = 2401.

Explanation

To find the unknown value in the given algebraic expression, simplify each part step by step using basic arithmetic rules and identities. First, compute the right-hand side of the equation: (150)² - (80)² - 737 Using the difference of squares identity, a² - b² = (a - b)(a + b): (150)² - (80)² = (150 - 80) × (150 + 80) = 70 × 230 = 16100 Now, subtract 737 from 16100: 16100 - 737 = 15363 Next, compute the square term on the left-hand side: (98)² = (100 - 2)² = 10000 - 400 + 4 = 9604 Substitute these simplified values back into the equation: 9604 + x = 15363 Isolate x by subtracting 9604 from 15363: x = 15363 - 9604 = 5759.

Explanation

To solve this arithmetic problem, apply the BODMAS rule, which dictates the correct order of operations: Brackets, Orders, Division/Multiplication, and Addition/Subtraction. First, execute the multiplication operation before performing addition or subtraction: 8 × 0.75 = 8 × (3 ÷ 4) = 6 Now, substitute this result back into the original expression: 48 + 6 - 5 Perform the addition and subtraction sequentially from left to right: 48 + 6 = 54 54 - 5 = 49.

Explanation

To evaluate the given decimal expression, combine the numbers being subtracted before taking them away from the initial decimal value. First, calculate the sum of all negative terms: 7.549 + 4.111 + 1.630 Adding these step by step: 7.549 + 4.111 = 11.660 11.660 + 1.630 = 13.290 Now, subtract this total sum from the starting positive decimal value: 18.657 - 13.290 = 5.367.

Explanation

To determine the unknown value, follow the standard BODMAS rule for order of mathematical operations, which prioritizes division over addition. First, evaluate the division term: 2950 ÷ 12.5 To simplify division by a decimal, rewrite 12.5 as 25 ÷ 2: 2950 ÷ (25 ÷ 2) = (2950 × 2) ÷ 25 = 5900 ÷ 25 = 236 Next, add 160 to this calculated value: 236 + 160 = 396.

Explanation

Items sold by seller A on Monday = 98 Items sold by seller A on Tuesday = 78

Average = (98 + 78) / 2 = 176 / 2 = 88

Explanation

Items sold by B on Wednesday = 60 Items sold by C on Wednesday = 82

Difference = 82 - 60 = 22

Explanation

Items sold by C on Tuesday = 90 Sum of items sold by B on Tuesday and A on Wednesday = 55 + 45 = 100

Required percentage = (90 / 100) × 100 = 90%

Explanation

Total items sold by B on Wednesday = 60 Ratio of defective to non-defective items = 1 : 5 (Total 6 ratio units)

Defective items = (1 / 6) × 60 = 10 Non-defective items = (5 / 6) × 60 = 50

Difference = 50 - 10 = 40

Explanation

Total items sold on Tuesday = 78 + 55 + 90 = 223 Total items sold on Wednesday = 45 + 60 + 82 = 187

Difference = 223 - 187 = 36

Explanation

Let the amount invested in each scheme be P. Simple interest formula: SI = (P × R × T) / 100

Interest from Scheme X = (P × 10 × 3) / 100 = 0.30P Interest from Scheme Y = (P × 6 × 3) / 100 = 0.18P

Total interest = 0.30P + 0.18P = 0.48P = 4800 P = 4800 / 0.48 = 10000

Explanation

Let Riya's investment be R and Meena's investment be M. Total investment: R + M = 6000

Riya invested for 12 months, and Meena invested for 6 months. Profit ratio = (R × 12) : (M × 6) = 2R : M

Since the profit ratio is equal (1 : 1): 2R = M

Substitute M = 2R into the total investment equation: R + 2R = 6000 3R = 6000 R = 2000

Explanation

Speed of train in m/s = 90 × (5 / 18) = 25 m/s

Total distance covered in 24 seconds = 25 × 24 = 600 m Total distance = Length of train (L) + Length of platform (P)

Given P = L + 80: L + (L + 80) = 600 2L + 80 = 600 2L = 520 L = 260 m

Explanation

Percentage of income saved by Rohit = (1 - 0.25) × (1 - 0.20) × (1 - 0.15) = 0.75 × 0.80 × 0.85 = 0.51 = 51%

Rohit's monthly income = 9180 / 0.51 = 18000

Since the ratio of Rohit's income to Amit's income is 4 : 5: Amit's monthly income = (18000 / 4) × 5 = 22500

Explanation

Let the present ages of Arjun, Karan, and the mentor be A, K, and M respectively. Given K = 25 and A + K = M: A + 25 = M M - A = 25 --- (Equation 1)

Four years ago, Arjun's age was half of the mentor's age: A - 4 = 0.5 × (M - 4) 2A - 8 = M - 4 2A - M = 4 --- (Equation 2)

Adding Equation 1 and Equation 2: (M - A) + (2A - M) = 25 + 4 A = 29

Present age of mentor M = 29 + 25 = 54 Age of mentor after 1 year = 54 + 1 = 55

Explanation

Combined 1-day work rate of P, Q, and R is 1/9. 1-day work rate of P is 1/18 and that of Q is 1/27. 1-day work rate of R = 1/9 - (1/18 + 1/27) = 1/9 - 5/54 = 1/54. Therefore, R alone takes 54 days to complete the work.

Explanation

Let the cost price be CP. Marked price = 1.40 × CP. Discount = 25% of Marked price = 0.25 × 1.40 × CP = 0.35 × CP. Selling price = Marked price - Discount = 1.40 × CP - 0.35 × CP = 1.05 × CP. Profit = Selling price - CP = 0.05 × CP = 60. CP = 60 / 0.05 = 1200. Discount allowed = 0.35 × 1200 = 420.

Explanation

In 40 liters of total mixture with milk to water ratio 3:2: Milk = (3/5) × 40 = 24 liters. Water = (2/5) × 40 = 16 liters. After adding x liters of water, the new milk to water ratio is 3:5. 24 / (16 + x) = 3/5 24 × 5 = 3 × (16 + x) 120 = 48 + 3x 3x = 72 x = 24.

Explanation

Downstream speed = Boat speed + Stream speed = 20 km/h. Given Stream speed = 4 km/h. Boat speed in still water = 20 - 4 = 16 km/h. Upstream speed = Boat speed - Stream speed = 16 - 4 = 12 km/h. Time taken upstream = Distance / Upstream speed = 24 / 12 = 2 hours.

Explanation

Let length be L and breadth be b = L/2, so L = 2b. Perimeter = 2 × (L + b) = 2 × (2b + b) = 6b = 60 cm. b = 10 cm. L = 2 × 10 = 20 cm. Area = L × b = 20 × 10 = 200 sq. cm.

Explanation

The differences between consecutive terms in reverse order are consecutive perfect squares: 100 - 96 = 4 = 2² 96 - 87 = 9 = 3² 87 - 71 = 16 = 4² 71 - 46 = 25 = 5² 46 - ? = 36 = 6² Therefore, ? = 46 - 36 = 10.

Explanation

First-order differences between consecutive terms: 231 - 218 = 13 253 - 231 = 22 293 - 253 = 40 369 - 293 = 76

Second-order differences: 22 - 13 = 9 40 - 22 = 18 76 - 40 = 36

The second-order differences double at each step (9, 18, 36, 72). Next first-order difference = 76 + 72 = 148. Missing term = 369 + 148 = 517.

Explanation

The recurrence relation for consecutive terms is xₙ₊₁ = xₙ / 2 - 2: 1308 / 2 - 2 = 652 652 / 2 - 2 = 324 324 / 2 - 2 = 160 160 / 2 - 2 = 78 78 / 2 - 2 = 37

Therefore, the missing number is 652.

Explanation

First-order differences between terms: 71 - 64 = 7 81 - 71 = 10 96 - 81 = 15

Second-order differences: 10 - 7 = 3 15 - 10 = 5

The second-order differences increase by 2 each step (3, 5, 7, 9). Next first-order difference = 15 + 7 = 22. Missing term = 96 + 22 = 118. Verification: 118 + (22 + 9) = 118 + 31 = 149.

Explanation

The recurrence relation for the series is xₙ₊₁ = 3 × xₙ + 3: 18 × 3 + 3 = 57 57 × 3 + 3 = 174 174 × 3 + 3 = 525 525 × 3 + 3 = 1578 1578 × 3 + 3 = 4737

Therefore, the missing term is 4737.

Explanation

Evaluating the terms on the left-hand side gives 12² = 144, 16² = 256, and 7.5 × 12 = 90. Adding these together yields 144 + 256 + 90 = 490. On the right-hand side, the cube root of 216 is 6. Substituting this into the equation gives 490 = ?² + 6, which simplifies to ?² = 484. Taking the square root of 484 gives ? = 22.

Explanation

Rearranging the equation to solve for ? gives ? = 3 1/7 + 5 1/14 - 2 1/7. Subtracting 2 1/7 from 3 1/7 leaves 1. Adding 1 to 5 1/14 yields 6 1/14.

Explanation

First, calculate the known terms: 12.5 × 14 = 175, and 25% of 760 = 760 / 4 = 190. Substituting these values into the expression gives ? % of 37.5 + 175 = 190. Subtracting 175 from 190 gives ? % of 37.5 = 15. Writing ? % as ? / 100 gives (? / 100) × 37.5 = 15, which simplifies to ? = 1500 / 37.5 = 40.

Explanation

Simplify the left-hand side sum: 1246 + 1567 = 2813. Evaluate the terms on the right-hand side: 22² = 484 and the cube root of 1000 is 10, giving a total of 484 + 10 = 494. Substituting these into the equation gives 2813 - ? = 494. Solving for ? yields ? = 2813 - 494 = 2319.

Explanation

First, calculate 175.5 ÷ 6 = 29.25. Next, subtract 29.25 from 175.75 to get 146.5. The equation becomes (783 / ?) + 146.5 = 190. Subtracting 146.5 from both sides gives 783 / ? = 43.5. Dividing 783 by 43.5 gives ? = 18.

Explanation

Calculate 56% of 55 = 0.56 × 55 = 30.8, and 8² = 64. Substituting these into the equation gives 30.8 + ? % of 132.8 = 64. Subtracting 30.8 from 64 gives ? % of 132.8 = 33.2. Solving for ? gives ? = (33.2 × 100) / 132.8 = 3320 / 132.8 = 25.

Explanation

Evaluating the terms gives 17.5 × 16 = 280, 28² = 784, and √576 = 24. Substituting these into the equation gives 280 + ? = 784 - 24, which simplifies to 280 + ? = 760. Subtracting 280 from 760 yields ? = 480.

Explanation

Calculate each part: 32² = 1024, 80% of 317.5 = 254, and 36² = 1296. Substituting these into the equation gives (? / 32.5) + 1024 + 254 = 1296. Combining the constants on the left gives (? / 32.5) + 1278 = 1296. Subtracting 1278 from 1296 gives ? / 32.5 = 18. Multiplying 18 by 32.5 yields ? = 585.

Explanation

Calculate 5.25 × 18 = 94.5 and 12.25 × 8 = 98. Also, 14² = 196. Substituting these values into the equation gives 94.5 + 98 + ? = 196. Combining the numbers on the left yields 192.5 + ? = 196. Subtracting 192.5 from 196 gives ? = 3.5.

Explanation

First, calculate 41% of 2560 = 0.41 × 2560 = 1049.6, and 32% of 388.75 = 0.32 × 388.75 = 124.4. The left-hand side sum is 1049.6 + 124.4 = 1174. On the right-hand side, 34² = 1156. The equation becomes 1174 = 1156 + ?. Subtracting 1156 from 1174 gives ? = 18.

Explanation

Calculating the individual percentage values on the left side: 43% of 800 = (43 ÷ 100) × 800 = 344 36% of 750 = (36 ÷ 100) × 750 = 270

Adding these two values gives the left-hand sum: 344 + 270 = 614

Let the required percentage be x. Setting up the equation: (x ÷ 100) × 400 = 614 4x = 614 x = 614 ÷ 4 = 153.5

Explanation

Simplifying each term individually: 7777 ÷ 700 = 77.77 ÷ 7 = 11.11 7777 ÷ 1100 = 77.77 ÷ 11 = 7.07 5555 ÷ 500 = 55.55 ÷ 5 = 11.11

Substituting these calculated quotient values back into the main expression gives: 11.11 + 7.07 − 11.11

The first and last terms cancel each other out, leaving: 7.07

Explanation

Grouping the numbers to make computation simpler: (4345 − 3345) + (5625 + 7125)

First, subtract 3345 from 4345: 4345 − 3345 = 1000

Next, add 5625 and 7125: 5625 + 7125 = 12,750

Finally, sum the two intermediate results together: 1000 + 12,750 = 13,750

Explanation

Evaluating the terms inside the square root following the order of operations: 80 ÷ 5 × 8 = 16 × 8 = 128 17 × 5 = 85 128 + 85 − 17 = 196 √(196) = 14

Evaluating the cube root term: ∛343 = 7

Dividing the two results: 14 ÷ 7 = 2

Let the missing value be x. Setting up the equation: 2 = ⁴√x x = 2⁴ = 16

Explanation

Evaluating the left-hand side of the given equation: (4 ÷ 5) × (2 ÷ 3) × (7 ÷ 9) × 16,200

Simplifying by cancelling factors with 16,200: 16,200 ÷ (5 × 3 × 9) = 16,200 ÷ 135 = 120

Multiplying the numerators with the quotient: 4 × 2 × 7 × 120 = 56 × 120 = 6720

Setting up the equality with the unknown value x: 6720 = (1 ÷ 6) × x x = 6720 × 6 = 40,320