IBPS RRB Clerk Prelims 2025 Numerical Ability Questions with Solutions

Explanation

Total scooters sold by A and B = 200 + 420 = 620. Cars sold by D = 240. Ratio = 620 : 240 = 31 : 12.

Explanation

The number of scooters sold by D is 160, which represents 1 part of the ratio 1:2. Total scooters (sold + unsold) = 1 + 2 = 3 parts. Total scooters = 3 × 160 = 480.

Explanation

Cars sold by B = 120. Non-defective cars sold by B = 120 × (1 - 0.25) = 90. Scooters sold by C = 250. Required percentage = (90 / 250) × 100 = 36%.

Explanation

Total scooters sold by all five companies = 200 + 420 + 250 + 160 + 300 = 1330. Average number of scooters sold = 1330 / 5 = 266.

Explanation

Scooters sold by F = 200 × 1.20 = 240. Cars sold by F = 140 × (1 - 0.30) = 98. Total scooters and cars sold by F = 240 + 98 = 338.

Explanation

Let the Cost Price (CP) be C. Marked Price (MP) = 1.25 C. Selling Price (SP) = 1.20 C. Discount = MP - SP = 0.05 C. Given discount = Rs 20. 0.05 C = 20 ⇒ C = 20 / 0.05 = 400. The cost price is Rs 400.

Explanation

A's investment for 12 months = 2000 × 12 = 24,000. B's investment = (4000 × 6) + (6000 × 6) = 24,000 + 36,000 = 60,000. Ratio of profit share A : B = 24,000 : 60,000 = 2 : 5. B's share in total profit = (5 / 7) × 14,000 = 10,000.

Explanation

Let the quantity of water be W liters. Quantity of milk = W + 6 liters. Total volume = W + (W + 6) = 44 liters. 2W + 6 = 44 ⇒ 2W = 38 ⇒ W = 19 liters. Quantity of milk = 19 + 6 = 25 liters. To make the ratio of milk to water 1:1, water added must equal the difference in quantities, which is 25 - 19 = 6 liters.

Explanation

Speed of train = Distance / Time = 520 / 13 = 40 m/s. Total distance to cross the platform = Length of train + Length of platform = 520 + 130 = 650 m. Time taken = 650 / 40 = 16.25 seconds = 16 1/4 seconds.

Explanation

Circumference = 2 × π × r = 88 cm. 2 × (22 / 7) × r = 88 ⇒ r = 14 cm. Area of circle = π × r² = (22 / 7) × 14 × 14 = 616 cm².

Explanation

Let the present ages of A and B be 7x and 9x respectively. Six years ago, their ages were 7x - 6 and 9x - 6.

Setting up the proportion: (7x - 6) / (9x - 6) = 11 / 15

Cross-multiplying gives: 15(7x - 6) = 11(9x - 6) 105x - 90 = 99x - 66 6x = 24 x = 4

Present age of B = 9 × 4 = 36 years. Age of B three years from now = 36 + 3 = 39 years.

Explanation

Let total income be I. Rent expenditure = 0.20 × I Remaining income = 0.80 × I Groceries expenditure = 0.10 × 0.80 × I = 0.08 × I Total expenditure = 0.20 × I + 0.08 × I = 0.28 × I

Given total expenditure = ₹4200: 0.28 × I = 4200 I = 4200 / 0.28 = 15000

Amount saved = Total income - Total expenditure Amount saved = 15000 - 4200 = 10800

Explanation

Given that the cost of 6 pens + 9 pencils = ₹150. Multiplying by 2 gives the cost of 12 pens + 18 pencils = 2 × 150 = ₹300. Three-fourth of this total cost = (3/4) × 300 = ₹225.

Explanation

For three consecutive even numbers, the middle number is equal to their average, which is 106. Thus, the three consecutive even numbers are 104, 106, and 108. The second largest number is 106 and the largest number is 108. Average of 106 and 108 = (106 + 108) / 2 = 107.

Explanation

Using the net percentage change formula for successive changes a% and b%: Net change = a + b + (a × b) / 100

Substituting a = +10 and b = -5: Net change = 10 - 5 + (10 × -5) / 100 = 5 - 0.5 = +4.5%

A positive value represents an overall 4.5% increase.

Explanation

The pattern in the series follows alternate square additions and subtractions starting from 2²: 220 + 2² = 224 224 - 3² = 215 215 + 4² = 231 231 - 5² = 206 206 + 6² = 242

Replacing 225 with 224 satisfies the entire sequence.

Explanation

The differences between consecutive terms form a sequence of consecutive prime numbers: 121 + 2 = 123 123 + 3 = 126 126 + 5 = 131 131 + 7 = 138 138 + 11 = 149

Replacing 150 with 149 completes the pattern.

Explanation

The differences between consecutive terms increase by 2 in each step: 13 + 91 = 104 104 + 93 = 197 197 + 95 = 292 292 + 97 = 389 389 + 99 = 488

Replacing 380 with 389 maintains the constant difference increment of 2.

Explanation

The sequence is formed by adding a constant difference of 8 to each term: 322 + 8 = 330 330 + 8 = 338 338 + 8 = 346 346 + 8 = 354 354 + 8 = 362

Replacing 336 with 346 produces a constant difference of 8 throughout the series.

Explanation

The pattern followed in the series is term × 2 - 2: 3 × 2 - 2 = 4 4 × 2 - 2 = 6 6 × 2 - 2 = 10 10 × 2 - 2 = 18 18 × 2 - 2 = 34

Replacing 7 with 6 follows the rule across all terms.

Explanation

To solve for the unknown value in the expression 44% of 750 + ?³ = 546, calculate the percentage component first. 44% of 750 = (44 / 100) × 750 = 0.44 × 750 = 330

Now, substitute 330 into the original equation: 330 + ?³ = 546

Isolate the cubic term ?³ by subtracting 330 from 546: ?³ = 546 - 330 ?³ = 216

Taking the cube root of 216 yields: ? = ∛216 = 6

Explanation

Evaluating the given expression (48 × ?) + (52 × 6) = 80% of 840 step by step:

First, calculate the right-hand side of the equation: 80% of 840 = (80 / 100) × 840 = 672

Next, evaluate the known multiplication term on the left-hand side: 52 × 6 = 312

Now, substitute these calculated values back into the equation: 48 × ? + 312 = 672

Subtract 312 from 672 to isolate the term containing the variable: 48 × ? = 672 - 312 48 × ? = 360

Divide 360 by 48 to find the unknown value: ? = 360 / 48 = 7.5

Explanation

Express all base numbers in terms of powers of 2 to simplify the left-hand side of the equation. 32 = 2⁵, so (32)⁰.4 = (2⁵)⁰.4 = 2⁽5 × 0.4) = 2² 16 = 2⁴, so (16)⁰.3 = (2⁴)⁰.3 = 2⁽4 × 0.3) = 2¹·² 64 = 2⁶, so (64)⁰.2 = (2⁶)⁰.2 = 2⁽6 × 0.2) = 2¹·²

Now multiply these terms together using the exponent rule aᵐ × aⁿ = aᵐ⁺ⁿ: (32)⁰.4 × (16)⁰.3 × (64)⁰.2 = 2² × 2¹·² × 2¹·² = 2⁽2 + 1.2 + 1.2) = 2⁴·⁴

Equating exponents on both sides of 2⁴·⁴ = 2^? gives: ? = 4.4

Explanation

To find the value of the missing variable ?, simplify both sides of the equation ? × 1.3 × 6.5 = 1.17 × 195.

First, compute the product on the right-hand side: 1.17 × 195 = 228.15

Next, calculate the product of the numerical factors on the left-hand side: 1.3 × 6.5 = 8.45

Substitute these products back into the original equation: ? × 8.45 = 228.15

Isolate ? by dividing 228.15 by 8.45: ? = 228.15 / 8.45 = 27

Explanation

To solve the algebraic expression ?² + 114 - 24 × 5 = 163, apply the standard order of operations.

First, calculate the multiplication term: 24 × 5 = 120

Substitute 120 into the equation: ?² + 114 - 120 = 163

Simplify the constant terms on the left side: ?² - 6 = 163

Isolate ?² by adding 6 to both sides of the equation: ?² = 163 + 6 ?² = 169

Take the positive square root of 169: ? = √169 = 13

Explanation

Simplify the left side of the given equation (3/4) of (4/7) of 343 = ? × 21 by replacing 'of' with multiplication. (3/4) × (4/7) × 343

The factor 4 in the numerator and denominator cancels out: (3/7) × 343

Since 343 = 7³, dividing 343 by 7 gives 49: 3 × 49 = 147

Now set the simplified left-hand side equal to the right-hand side: 147 = ? × 21

Divide 147 by 21 to solve for ?: ? = 147 / 21 = 7

Explanation

According to standard BODMAS/PEMDAS rules, perform multiplication and division from left to right before subtraction.

Evaluate the given mathematical expression 60 × (2/4) - 26 step by step: First, simplify the fractional term 2/4 to 1/2.

Multiply 60 by 1/2: 60 × (1/2) = 30

Substitute this product back into the equation: 30 - 26 = ?

Subtract 26 from 30 to obtain the required value: ? = 4

Explanation

Evaluate both sides of the given percentage equation 66% of 350 + ? = (5/8) of 1256.

First, compute 66% of 350: (66 / 100) × 350 = 0.66 × 350 = 231

Next, calculate (5/8) of 1256: (5 / 8) × 1256 = 5 × 157 = 785

Substitute these evaluated quantities back into the main equation: 231 + ? = 785

Subtract 231 from 785 to isolate the unknown parameter ?: ? = 785 - 231 = 554

Explanation

Evaluate each component of the expression 15% of 300 + 9.09% of 803 + 3 = (?)² step by step.

First, calculate 15% of 300: (15 / 100) × 300 = 45

Next, convert 9.09% into its fractional equivalent, which is approximately 1/11: 9.09% of 803 ≈ (1 / 11) × 803 = 73

Now sum all the terms on the left side: 45 + 73 + 3 = 121

Set the sum equal to (?)²: (?)² = 121

Take the positive square root of 121: ? = √121 = 11

Explanation

Apply standard BODMAS/PEMDAS rules to evaluate 680 ÷ 17 × 15 = ?. Since division and multiplication carry the same precedence level, perform the operations strictly from left to right.

First, execute the division operation: 680 ÷ 17 = 40

Next, multiply the resulting quotient by 15: 40 × 15 = 600

Therefore, the calculated value that replaces the question mark is 600.

Explanation

Evaluating the left side of the equation gives 544 ÷ 8.5 = 544 ÷ (17/2) = (544 × 2) ÷ 17 = 64. Expressing 64 as a power of 2 gives 2⁶ = 64. Thus, the required value is 6.

Explanation

Simplifying the product of the first two terms gives (9/7)³ × (14/27)² = (729 / 343) × (196 / 729) = 196 / 343 = 4 / 7. Substituting this into the equation yields (4 / 7) × 7ˣ = 28, which simplifies to 7ˣ = (28 × 7) / 4 = 49. Since 49 = 7², the exponent x is equal to 2.

Explanation

Using √784 = 28, the expression is evaluated sequentially according to division rules: 28 ÷ (4/7) = 28 × (7/4) = 49. Next, dividing by 49 gives 49 ÷ 49 = 1.

Explanation

According to the order of operations (BODMAS), division is performed first: 320 ÷ 8 = 40. Then, performing addition and subtraction from left to right yields 635 - 28 + 40 = 607 + 40 = 647.

Explanation

Calculating the two terms individually gives 35% of 250 = (35/100) × 250 = 87.5, and 25% of 35 = (25/100) × 35 = 8.75. Adding the two results together gives 87.5 + 8.75 = 96.25.

Explanation

Total marks scored by P and Q in English = 120 + 100 = 220. Marks scored by S in Maths = 110. Required ratio = 220 : 110 = 2 : 1.

Explanation

Total marks scored by P and T in Hindi = 100 + 80 = 180. Total marks scored by S in English and Hindi = 50 + 150 = 200. Required percentage = (180 / 200) × 100 = 90%.

Explanation

Total marks scored by P in all subjects = 120 + 100 + 130 = 350. Total marks scored by R in all subjects = 80 + 130 + 90 = 300. Total marks obtained by A = 350 + 300 = 650. The marks obtained by A in English, Hindi, and Maths are in the ratio 3 : 6 : 4. Sum of ratio terms = 3 + 6 + 4 = 13 parts. Value of 1 part = 650 / 13 = 50. Marks obtained by A in English = 3 × 50 = 150.

Explanation

Sum of marks scored in Hindi by P, Q, R, S, and T = 100 + 132 + 130 + 150 + 80 = 592. Average marks = 592 / 5 = 118.4.

Explanation

Total marks scored by T and Q in English = 40 + 100 = 140. Total marks scored by R and S in Hindi = 130 + 150 = 280. Required difference = 280 - 140 = 140.

Explanation

In a 42-liter mixture with milk and water in the ratio 2:5, total ratio parts = 7. Initial milk = (2 / 7) × 42 = 12 liters. Initial water = (5 / 7) × 42 = 30 liters. Let x liters of milk be added. The new ratio of water to milk is 1:4. 30 / (12 + x) = 1 / 4 12 + x = 120 x = 108 liters.

Explanation

Let the total work be 180 units. Efficiency of A + B = 180 / 15 = 12 units/day. Efficiency of B = 180 / 36 = 5 units/day. Efficiency of A = 12 - 5 = 7 units/day. Let total time taken to finish the work be T days. Since B left 6 days before completion, A worked for T days and B worked for (T - 6) days. 7T + 5(T - 6) = 180 12T - 30 = 180 12T = 210 T = 17.5 days.

Explanation

Let the length of the rectangle be L and breadth be b. b = L - 0.25L = 0.75L = 3L / 4. Perimeter = 2(L + b) = 70 cm. L + 3L / 4 = 35 7L / 4 = 35 L = 20 cm. b = 15 cm. Area = L × b = 20 × 15 = 300 cm².

Explanation

Let CP be the cost price and MP be the marked price. MP = CP + 1900. Selling Price (SP) = MP - 0.20 × MP = 0.80 MP. SP = 0.80(CP + 1900) = 0.80 CP + 1520. Profit = SP - CP = 450. (0.80 CP + 1520) - CP = 450 1520 - 0.20 CP = 450 0.20 CP = 1070 CP = 1070 / 0.20 = 5350.

Explanation

Speed of A = 54 / 2 = 27 km/h. Since speed of A is 20% more than speed of B: Speed of A = 1.2 × Speed of B 27 = 1.2 × Speed of B Speed of B = 22.5 km/h. Distance travelled by B in 4 hours = 22.5 × 4 = 90 km.

Explanation

Boat speed in still water = Upstream speed + Stream speed = 6 + 2 = 8 km/hr. Downstream speed = Boat speed + Stream speed = 8 + 2 = 10 km/hr. Time taken to cover 80 km downstream = Distance / Downstream speed = 80 / 10 = 8 hours.

Explanation

The profit sharing ratio depends on the product of investment and time: A's share = 2800 × 8 = 22400 B's share = 5400 × 12 = 64800 C's share = 3600 × 12 = 43200 Ratio A : B : C = 22400 : 64800 : 43200 = 28 : 81 : 54. Total ratio units = 28 + 81 + 54 = 163. Since 81 ratio units equal Rs 2430, 1 ratio unit equals 2430 / 81 = Rs 30. Total profit = 163 × 30 = Rs 4890.

Explanation

Compound interest for 3 years at 10% p.a. is given by CI = X × ((1 + 0.10)³ - 1) = 0.331 X. 0.331 X = 1324 gives X = 4000. Simple interest principal = X + 500 = 4000 + 500 = Rs 4500. Simple interest = (P × R × T) / 100 = (4500 × 15 × 2) / 100 = Rs 1350.

Explanation

Let the total tank capacity be 60 units (LCM of 15 and 20). Efficiency of Pipe A = 60 / 15 = 4 units/hour. Efficiency of Pipe B = 60 / 20 = 3 units/hour. Work completed in the first 4 hours by both pipes = (4 + 3) × 4 = 28 units. Remaining work = 60 - 28 = 32 units. Time taken by Pipe B to finish remaining work = 32 / 3 = 10 ⅔ hours. Total time taken = 4 + 10 ⅔ = 14 ⅔ hours.

Explanation

Total distance to cover = Sum of train lengths = 180 + 120 = 300 m. Relative speed in opposite directions = 54 + 72 = 126 km/h. Converting relative speed to m/s = 126 × (5 / 18) = 35 m/s. Time taken to cross each other = 300 / 35 = 60/7 seconds.