IBPS RRB Clerk Prelims 2024 Numerical Ability Questions with Solutions

Explanation

Simple interest SI = P × R × T / 100. 1560 = P × 12 × 5 / 100 1560 = 0.6 × P P = 2600 Difference between principal and simple interest = P - SI = 2600 - 1560 = 1040.

Explanation

From the average of X, Y, and Z, X + Y + Z = 27. Since half of Y is 5, Y = 10. Substituting Y = 10 into the sum gives X + Z = 17. Given Z - X = 5, adding the two equations yields 2Z = 22, which gives Z = 11.

Explanation

Let Jerry's present age be J and Tom's present age be T. J = T + 16 Four years hence, (J + 4) / (T + 4) = 11 / 7. Substituting J = T + 16 gives (T + 20) / (T + 4) = 11 / 7. 7(T + 20) = 11(T + 4) 7T + 140 = 11T + 44 4T = 96 T = 24 Jerry's present age J = 24 + 16 = 40 years.

Explanation

A's 1-day work = 1/15. A and B together complete 3/5th of work in 4 days, so they complete the whole work in 4 × 5/3 = 20/3 days. Their combined 1-day work = 3/20. B's 1-day work = 3/20 - 1/15 = (9 - 4) / 60 = 5/60 = 1/12. Therefore, B alone can complete the whole work in 12 days.

Explanation

Since B has 78% more chocolates than A, B = 1.78 × A. Given B = 89, substituting into the equation gives 1.78 × A = 89. A = 89 / 1.78 = 50.

Explanation

The pattern in the series is cubes of consecutive prime numbers: 2³ = 8 3³ = 27 5³ = 125 7³ = 343 11³ = 1331 13³ = 2197 17³ = 4913 The number 121 is given instead of 1331, making it the wrong number in the series.

Explanation

The pattern in the series is dividing each successive number by 2: 3264 ÷ 2 = 1632 1632 ÷ 2 = 816 816 ÷ 2 = 408 408 ÷ 2 = 204 204 ÷ 2 = 102 102 ÷ 2 = 51 The term 206 should be 204, making 206 the wrong number in the series.

Explanation

The pattern in the series is multiplying by 2 and adding 1: 20 × 2 + 1 = 41 41 × 2 + 1 = 83 83 × 2 + 1 = 167 167 × 2 + 1 = 335 335 × 2 + 1 = 671 671 × 2 + 1 = 1343 The number 670 is given instead of 671, making it the wrong number in the series.

Explanation

The pattern in the series is subtracting 17 from each preceding term: 203 - 17 = 186 186 - 17 = 169 169 - 17 = 152 152 - 17 = 135 135 - 17 = 118 118 - 17 = 101 The number 104 is given instead of 101, making it the wrong number in the series.

Explanation

The pattern in the series is multiplying each successive number by 2: 27 × 2 = 54 54 × 2 = 108 108 × 2 = 216 216 × 2 = 432 432 × 2 = 864 864 × 2 = 1728 The term 214 is given instead of 216, making 214 the wrong number in the series.

Explanation

Start with (?+3)/5 + 5/15 = 24/15. Simplify 5/15 to 1/3, and rewrite (?+3)/5 with denominator 15, giving 3(?+3)/15 + 5/15 = 24/15. Multiplying through by 15 gives 3(?+3) + 5 = 24, so 3(?+3) = 19. Dividing by 3 gives ?+3 = 19/3, so ? = 19/3 - 9/3 = 10/3.

Explanation

Simplifying each term gives 5/4 + 3 - 1 + 2 = 5/4 + 4 = 21/4, which equals 5.25.

Explanation

(5/6) × (8/7) × (21/24) × 2526 = (5/6) × 1 × 2526 = 5 × 421 = 2105.

Explanation

5² + 13² - 11² + 52 = 25 + 169 - 121 + 52 = 125. Taking the cube root of 125 gives 5.

Explanation

Simplify the left side first: 252/121 × 22/9 reduces because 121 = 11 × 11 and 22 = 2 × 11, giving 252 × 2/(11 × 9) = 56/11. Multiplying by 114/333, and noting 114/333 reduces to 38/111, gives (38/111) × (56/11) = 2128/1221. On the right side, 28/37 × 19/x = 532/(37x). Setting 2128/1221 equal to 532/(37x) and cross-multiplying gives 2128 × 37x = 532 × 1221, and since 1221 = 33 × 37, this simplifies to 2128x = 532 × 33, so x = 17556/2128 = 8.25.

Explanation

19² - 23 × 12 = 361 - 276 = 85. The right side simplifies to ?² + 256 ÷ 64 = ?² + 4. Solving 85 = ?² + 4 gives ?² = 81, so ? = 9.

Explanation

√(587 + 638) ÷ 25 + ? = 2828 ÷ 7 simplifies to √(1225 ÷ 25) + ? = 404, which reduces to √49 + ? = 404. Thus, 7 + ? = 404, giving ? = 397.

Explanation

42% of 800 = 336 and 19² = 361. The equation becomes 336 + 725/? = 361. Subtracting 336 from 361 gives 725/? = 25, so ? = 725 / 25 = 29.

Explanation

Simplify the right-hand side: 13/260 reduces to 1/20 and 80/480 reduces to 1/6. Taking a common denominator of 60 gives 3/60 + 10/60 = 13/60. The equation is therefore ?/2 = 13/60, so ? = 2 x 13/60 = 26/60. Reducing gives ? = 13/30.

Explanation

18² = 324 and (40% of 200) / 5 = 80 / 5 = 16. The left-hand side sums to 324 + 16 = 340. Setting 340 = 17/? gives ? = 17 / 340 = 1/20.

Explanation

To evaluate the given mathematical expression, simplify the individual components using power and root properties: ∛3375 = 15 5² = 25

Now substitute these values back into the simplified fraction form: 3 / 15 = 1 / 5 80 / 25 = 16 / 5

Next, perform the division of the two fractions by multiplying the first fraction by the reciprocal of the second: (1 / 5) ÷ (16 / 5) = (1 / 5) × (5 / 16) = 1 / 16

Explanation

To find the unknown value, simplify each component on the left-hand side of the equation using the order of operations:

First, calculate (5 / 9) of 180: (5 / 9) × 180 = 5 × 20 = 100

Next, calculate the square term: 8² = 64

Add these terms together to find the value of the left-hand side: 100 + 64 = 164

Set up the linear equation for the unknown value: 164 = ? - 24 ? = 164 + 24 = 188

Explanation

To evaluate the arithmetic expression, combine the positive and negative terms step by step following standard order of operations:

First, add the positive terms: 318 + 980 = 1298

Next, subtract the first negative term: 1298 - 224 = 1074

Finally, subtract the second negative term: 1074 - 540 = 534

Alternatively, group the additions and subtractions: (318 + 980) - (224 + 540) = 1298 - 764 = 534

Explanation

To solve for the unknown variable, first simplify the left-hand side by cancelling common factors:

(224 / 49) × (7 / 16)

Cancel 7 in the numerator and 49 in the denominator: (224 / 7) × (1 / 16) = 32 × (1 / 16) = 32 / 16 = 2

Now set the simplified left-hand side equal to the right-hand side: 2 = 5 × ?

Isolate the question mark by dividing both sides by 5: ? = 2 / 5

Explanation

To find the unknown value, evaluate both sides of the equation using percentage and exponent identities:

First, calculate the cube: 12³ = 1728

Subtract 728 to find the value of the left-hand side: 1728 - 728 = 1000

Next, convert 33.33% to its equivalent fraction 1/3: 33.33% of 69 = (1 / 3) × 69 = 23

Set up the simplified equation: 1000 = ? + 23

Isolate the unknown value by subtracting 23 from 1000: ? = 1000 - 23 = 977

Explanation

Total marks obtained in 5 subjects = 5 × 105 = 525. The average of the 3 subjects excluding highest and lowest is 72, so their sum = 3 × 72 = 216. Sum of highest and lowest marks = Total marks - Sum of remaining 3 subjects = 525 - 216 = 309.

Explanation

Work done by 1 bull in 1 day = 1 / (6 × 9) = 1/54. Work done by 1 ox in 1 day = 1 / (12 × 6) = 1/72. Combined daily work rate of 5 bulls and 4 oxen = 5 × (1/54) + 4 × (1/72) = 5/54 + 1/18 = (5 + 3)/54 = 8/54 = 4/27. Number of days required to complete the field = 1 / (4/27) = 27/4 = 6.75 days (or 6 ¾ days).

Explanation

Let the breadth of the rectangle be B cm. Then length L = B + 3 cm. Perimeter = 2(L + B) = 66 2(B + 3 + B) = 66 2B + 3 = 33 2B = 30 ⇒ B = 15 cm Length L = 15 + 3 = 18 cm. Area of rectangle = L × B = 18 × 15 = 270 cm².

Explanation

Let the initial quantities of milk and water be 11x and 8x liters respectively. After adding 8 liters of milk and 24 liters of water: (11x + 8) / (8x + 24) = 7 / 6 Cross-multiplying: 6(11x + 8) = 7(8x + 24) 66x + 48 = 56x + 168 10x = 120 ⇒ x = 12 Initial quantity of water = 8x = 8 × 12 = 96 liters.

Explanation

Let the bigger number be B and smaller number be S. Given, S = ½ B + 13 ⇒ B = 2S - 26. Also, B - S = 78. Substituting B into the difference equation: (2S - 26) - S = 78 S - 26 = 78 ⇒ S = 104.

Explanation

Given X = Y + 24, so Y = X - 24. Also, ⅗ X = Y - 16. Substituting Y = X - 24: ⅗ X = (X - 24) - 16 ⅗ X = X - 40 X - ⅗ X = 40 ⅖ X = 40 ⇒ X = 100. Therefore, Y = 100 - 24 = 76.

Explanation

Present age of A = 21 + 3 = 24 years. Age of A after 4 years = 24 + 4 = 28 years. Ratio of ages of A to B after 4 years = 7 : 5. Let age of B after 4 years be B₄. 28 / B₄ = 7 / 5 ⇒ B₄ = 20 years. Present age of B = 20 - 4 = 16 years.

Explanation

Profit ratio of P and Q = (Investment of P × Time) : (Investment of Q × Time) (2500 × 12) / (X × 8) = 5 / 4 30000 / 8X = 5 / 4 3750 / X = 5 / 4 5X = 15000 ⇒ X = 3000.

Explanation

Simple Interest SI = (P × R × T) / 100 2700 = (P × 12 × 5) / 100 2700 = 60P / 100 2700 = 0.6P P = 2700 / 0.6 = 4500 Rs.

Explanation

Distance covered by car = 2 × 60 = 120 km. Distance covered by bus = 5 × 80 = 400 km. Distance covered by bicycle = 5 × 10 = 50 km. Total distance = 120 + 400 + 50 = 570 km. Total time = 2 + 5 + 5 = 12 hours. Average speed = Total distance / Total time = 570 / 12 = 47.5 km/hr.

Explanation

The pattern in the series is based on adding increments that increase by 2.5 at each step: 24.5 - 22 = 2.5 29.5 - 24.5 = 5.0 37 - 29.5 = 7.5 47 - 37 = 10.0 The next difference is 10.0 + 2.5 = 12.5. Adding this to the last term yields 47 + 12.5 = 59.5.

Explanation

The differences between successive terms are squares of descending prime numbers: 413 - 244 = 169 = 13² 244 - 123 = 121 = 11² 123 - 74 = 49 = 7² The next prime in descending order is 5, so the required subtraction is 5² = 25. 74 - 25 = 49. Subtracting the next prime square 3² = 9 confirms 49 - 9 = 40.

Explanation

The difference between terms follows a geometric progression with a common ratio of 3: 68 - 64 = 4 80 - 68 = 12 = 4 × 3 116 - 80 = 36 = 12 × 3 224 - 116 = 108 = 36 × 3 The next difference is 108 × 3 = 324. Adding this difference to 224 gives 224 + 324 = 548.

Explanation

The differences between adjacent terms increase by 10 at each step: 22 - 17 = 5 37 - 22 = 15 62 - 37 = 25 The next difference in the sequence is 25 + 10 = 35. Adding this to 62 gives 62 + 35 = 97. Continuing the pattern with 35 + 10 = 45 gives 97 + 45 = 142, confirming the calculation.

Explanation

Examining the differences between adjacent terms from the right end of the series shows: 823 - 423 = 400 423 - 223 = 200 223 - 123 = 100 Halving the difference for each preceding step gives 50 and 25. The missing term is 123 - 50 = 73. Checking the first step gives 73 - 48 = 25, which confirms the pattern.

Explanation

Total students in class B and C together in May = 80 + 68 = 148. Total students in class A and C together in March = 96 + 91 = 187. Required difference = 187 - 148 = 39.

Explanation

Total students in class C for March, April, and May = 91 + 60 + 68 = 219. Average number of students in class C for these months = 219 / 3 = 73. Total students in class A in June = 75. Percentage = (73 / 75) × 100 = 97.33%, which rounds to approximately 97%.

Explanation

Total students in class A and B in April = 64 + 72 = 136. Students in class D in April = 136 / 2 = 68. Students in class B in March = 87. Required sum = 68 + 87 = 155.

Explanation

Students in class A in May = 90. Sum of students in class B in May and class C in April = 80 + 60 = 140. Required ratio = 90 : 140 = 9 : 14.

Explanation

Students in class A in March = 96. Students in class B in June = 63. Difference = 96 - 63 = 33. Percentage more = (33 / 63) × 100 = (11 / 21) × 100 = 52.38%, which rounds to 52%.

Explanation

Simplifying the fraction 209/399 by dividing numerator and denominator by 19 yields 11/21. Substituting this back into the expression: (11/21) × 21² - 11² = 11 × 21 - 121 = 231 - 121 = 110.

Explanation

First, add the numbers on the left-hand side: 343 + 243 + 512 = 1098. Let the required value be x. 20% of x = (20/100) × x = x / 5 = 1098. x = 1098 × 5 = 5490.

Explanation

Evaluating each root individually: ∛1728 = 12, √784 = 28, √1296 = 36, and ∛512 = 8. Substitute these values into the equation: 12 + 28 + 36 = ? + 8 76 = ? + 8 ? = 76 - 8 = 68.

Explanation

Evaluating each term: √(256 × 49) = √256 × √49 = 16 × 7 = 112 16² = 256 ∛343 = 7 Substituting these into the expression: 112 + 256 - 7 = (?)² 361 = (?)² ? = √361 = 19.

Explanation

Convert the mixed fractions on the left side: 7 + 4/5 - (3 + 2/3) + 4 + 8/15 Separate integer and fractional parts: (7 - 3 + 4) + (4/5 - 2/3 + 8/15) = 8 + (12 - 10 + 8)/15 = 8 + 10/15 = 8 + 2/3 = 26/3. Setting this equal to 234/?: 26/3 = 234/? ? = (234 × 3) / 26 = 9 × 3 = 27.