IBPS RRB Clerk Prelims 2016 Numerical Ability Questions with Solutions

Explanation

Simplify the sum inside the parentheses: 364 + 514 = 878

Set up the equation with division: (878 - ?) ÷ 4 = 200 878 - ? = 200 × 4 = 800 ? = 878 - 800 = 78

Explanation

Let March salary be S. Remaining salary after spending 45% on bill and rent = 100% - 45% = 55% of S. Amount deposited in bank = 100% - 60% = 40% of remaining salary = 0.40 × 0.55 × S = 0.22 S.

Given 0.22 S = ₹15,400: S = 15,400 ÷ 0.22 = ₹70,000

In April, salary increased by 10%: April salary = 70,000 × 1.10 = ₹77,000

Explanation

Calculate total distance using Distance = Speed × Time: Time = 90 min = 1.5 hours Distance = 120 km/h × 1.5 h = 180 km

Convert target time to hours: 1 hour 20 min = 1 + 20/60 = 4/3 hours

Calculate required speed = Distance ÷ Time: Speed = 180 ÷ (4/3) = 180 × (3 / 4) = 135 km/h

Explanation

Initial ratio of milk to water in Jar A is 120 : 24 = 5 : 1. When 12 litres of mixture is removed, milk removed is 12 × (5/6) = 10 litres, and water removed is 12 × (1/6) = 2 litres. Remaining milk = 110 litres, and remaining water = 22 litres. After adding 3 litres of water, new water quantity = 25 litres, and total mixture = 135 litres. The new milk to water ratio is 110 : 25 = 22 : 5. When 27 litres of this new mixture is removed, water removed is 27 × (5/27) = 5 litres. The resultant quantity of water remaining in Jar A = 25 - 5 = 20 litres.

Explanation

The formula for total time taken in round-trip boat motion is Total Time = Distance / (u + v) + Distance / (u - v), where u is boat speed in still water and v is stream speed. Given distance = 30 km, u = 15 km/h, and total time = 4.5 hours: 30 / (15 + v) + 30 / (15 - v) = 4.5 30 × (15 - v + 15 + v) / (225 - v²) = 4.5 900 / (225 - v²) = 4.5 225 - v² = 200 v² = 25 v = 5 km/h.

Explanation

Let the ages of Kunal and Sagar six years ago be 6x and 5x respectively. Their present ages are 6x + 6 and 5x + 6. Four years hence, their ages will be 6x + 10 and 5x + 10. According to the given ratio: (6x + 10) / (5x + 10) = 11 / 10 10 × (6x + 10) = 11 × (5x + 10) 60x + 100 = 55x + 110 5x = 10 x = 2 Sagar's present age = 5x + 6 = 5(2) + 6 = 16 years.

Explanation

The problem provides two algebraic equations: X = Y + 150 and X + Y = 5Y. Substituting X from the first equation into the second equation yields: (Y + 150) + Y = 5Y 2Y + 150 = 5Y Subtracting 2Y from both sides gives: 3Y = 150 Y = 50.

Explanation

The formula for the area of a square is side², which gives the length of one side as the square root of the area. side = √50625 = 225 metres. The boundary length needing fencing is the perimeter of the square, calculated as: Perimeter = 4 × side = 4 × 225 = 900 metres. Multiplying the perimeter by the fencing rate gives: Total Cost = 900 × ₹15 = ₹13,500.

Explanation

When one person is replaced by a new person, the change in total weight equals the total number of persons multiplied by the increase in average weight. Increase in total weight = Number of persons × Increase in average Increase in total weight = 8 × 2.5 = 20 kg. Weight of new person = Weight of replaced person + Increase in total weight Weight of new person = 65 + 20 = 85 kg.

Explanation

Let the unknown number be x. Expressing 50% of the number gives ½x, and two-third of the number gives ⅔x. According to the given condition, ⅔x - ½x = 18. Taking the common denominator of 6, we get (4 - 3)x / 6 = 18, which simplifies to x / 6 = 18. Multiplying both sides by 6 yields x = 108.

Explanation

The total number of prime numbers from 1 to 20 is 8 (which are 2, 3, 5, 7, 11, 13, 17, 19). The total number of ways to draw 2 tickets out of 20 is given by 20C2 = (20 × 19) / 2 = 190. The number of favorable ways to draw 2 prime tickets from the 8 prime numbers is 8C2 = (8 × 7) / 2 = 28. Probability = Favorable outcomes / Total outcomes = 28 / 190 = 14 / 95.

Explanation

From the table, the number of people who watched movie X on Monday is 30 and on Wednesday is 36, giving a total of 30 + 36 = 66. Similarly, the number of people who watched movie Z on Monday is 50 and on Wednesday is 56, giving a total of 50 + 56 = 106. The ratio between the total number of people who watched movie X on Monday and Wednesday together to those who watched movie Z on the same days together is 66 : 106, which simplifies to 33 : 53.

Explanation

To find the required difference, sum the viewers for movies X and Z on each specified day from the table. On Tuesday: Viewers of X = 34, Viewers of Z = 55. Total = 34 + 55 = 89. On Thursday: Viewers of X = 30, Viewers of Z = 60. Total = 30 + 60 = 90. Difference = 90 - 89 = 1.

Explanation

The total number of people who watched movie W on Monday, Wednesday, and Friday is obtained by summing the respective values from the table: Monday = 28 Wednesday = 18 Friday = 32 Sum = 28 + 18 + 32 = 78. Average viewers = Sum of viewers / Number of days = 78 / 3 = 26.

Explanation

From the table, the number of people who watched movie Y on Wednesday is 55, and the number of people who watched movie Y on Friday is 32. To calculate the percentage: Percentage = (Movie Y on Wednesday / Movie Y on Friday) × 100 Percentage = (55 / 32) × 100 = 171.875%. Rounding off to the nearest whole integer yields 172%.

Explanation

From the table, the number of people who watched movie Z on Friday is 68. Adding 32 to this value gives 68 + 32 = 100 people who watched movie Z on Saturday.

Explanation

The effective compound interest rate for 2 years at 10% per annum is 10 + 10 + (10 × 10)/100 = 21%. Given CI = ₹525, the principal P = 525 / 0.21 = ₹2500. For simple interest, the new time is T = 2 × 2 = 4 years, and the new rate is R = 10 / 2 = 5%. Simple Interest = (P × R × T) / 100 = (2500 × 5 × 4) / 100 = ₹500.

Explanation

Perimeter of the rectangle = 2 × (18 + 26) = 88 cm. Since the circle has the same perimeter, 2 × (22/7) × r = 88 cm, which yields a radius r = 14 cm. Area of the circle = πr² = (22/7) × 14² = 616 cm² = 0.0616 m².

Explanation

The differences between consecutive terms in the series 12, 13, 17, 26, 42 are 1, 4, 9, and 16, which correspond to 1², 2², 3², and 4². Adding the next square number, 5² = 25, to 42 gives 42 + 25 = 67.

Explanation

The pattern in the series involves multiplying each term by consecutive even numbers: 1 × 2 = 2 2 × 4 = 8 8 × 6 = 48 48 × 8 = 384 384 × 10 = 3840

Explanation

The pattern is formed by subtracting consecutive multiples of 7 from each term: 157 - 7 = 150 150 - 14 = 136 136 - 21 = 115 115 - 28 = 87 87 - 35 = 52

Explanation

First-level differences are: 4 - 1 = 3 18 - 4 = 14 44 - 18 = 26 83 - 44 = 39

Second-level differences are: 14 - 3 = 11 26 - 14 = 12 39 - 26 = 13

Continuing the second difference pattern with 14: 39 + 14 = 53 83 + 53 = 136

Explanation

The multiplier increases by 0.5 at each step: 8 × 0.5 = 4 4 × 1 = 4 4 × 1.5 = 6 6 × 2 = 12 12 × 2.5 = 30

Explanation

80.137 × 9 = 721.233 2.11 × 139.7 = 294.767 721.233 + 294.767 = 1016

Explanation

7802 + 132 - 8963 + 1326 = ? × 33 7934 - 8963 + 1326 = ? × 33 -1029 + 1326 = ? × 33 297 = ? × 33 ? = 297 ÷ 33 = 9

Explanation

21.9% of 650 = (21.9 × 650) / 100 = 142.35 142.35 = ? + 23.12 ? = 142.35 - 23.12 = 119.23

Explanation

Applying order of operations from left to right: 6666 ÷ 66 = 101 101 ÷ 0.25 = 101 × 4 = 404

Explanation

√2704 = 52 √? + 18 = 52 √? = 52 - 18 = 34 ? = 34² = 1156

Explanation

217 + 435 - 317 + 5110 = (217 - 317) + 435 + 5110 = -100 + 435 + 5110 = 335 + 5110 = 5445

Explanation

According to the order of operations (BODMAS), multiplication is performed before subtraction.

First, calculate the product of 164 and 43: 164 × 43 = 164 × (40 + 3) = (164 × 40) + (164 × 3) = 6560 + 492 = 7052

Next, subtract 6070 from the calculated product: 7052 - 6070 = 982

Explanation

To solve for the missing value, first calculate the value of the given percentage term on the left side: 14.5% of 740 = (14.5 / 100) × 740 = 0.145 × 740 = 107.3

Substitute 107.3 into the equation in place of the first term: 107.3 - ?% of 320 = 87.3

Rearrange the equation to isolate the term containing the question mark: ?% of 320 = 107.3 - 87.3 = 20

Express the percentage as a fraction and solve for ?: (? / 100) × 320 = 20 ? = (20 × 100) / 320 = 2000 / 320 = 6.25

Explanation

Convert every term to base 3: 27 = 3³, so (27)³ = 3⁹, and 81 = 3⁴, so (81)² = 3⁸. The expression becomes 3⁹ × 3⁴ ÷ 3⁸. Adding the exponents in the numerator gives 3¹³, then dividing by 3⁸ gives 3¹³⁻⁸ = 3⁵. Equating this to 3^? gives ? = 5.

Explanation

First, evaluate the two products on the left-hand side of the equation: 37.135 × 25 = 928.375 125 × 1.061 = 132.625

Add the two results together to simplify the left-hand side: 928.375 + 132.625 = 1061

Substitute this total back into the original equation: 1061 = √? + 894

Isolate the square root term by subtracting 894 from both sides: √? = 1061 - 894 = 167

Square both sides of the equation to find the value of ?: ? = 167² = (170 - 3)² = 28900 - 1020 + 9 = 27889

Explanation

Simplify the numerical expression on the left-hand side of the equation by performing the operations sequentially from left to right: 4376 + 3209 = 7585 7585 - 1784 = 5801 5801 + 97 = 5898

Now set up the equation with the simplified left-hand side: 5898 = 3125 + ?

Isolate the unknown variable ? by subtracting 3125 from 5898: ? = 5898 - 3125 = 2773

Explanation

First, calculate the square root on the right-hand side of the equation: √2601 = 51

Substitute 51 back into the equation: √? + 14 = 51

Subtract 14 from both sides of the equation to isolate the square root term: √? = 51 - 14 = 37

To solve for ?, square both sides of the equation: ? = 37² = (40 - 3)² = 1600 - 240 + 9 = 1369

Explanation

First, calculate the value of the known percentage term: 85% of 420 = (85 / 100) × 420 = 0.85 × 420 = 357

Substitute this value into the equation: 357 + ?% of 1080 = 735

Subtract 357 from 735 to isolate the unknown percentage expression: ?% of 1080 = 735 - 357 = 378

Solve for the unknown value ?: (? / 100) × 1080 = 378 ? = (378 × 100) / 1080 = 3780 / 108 = 35

Explanation

Following the standard order of operations (BODMAS), perform division first, followed by multiplication, and lastly subtraction.

First, divide 3024 by 54: 3024 ÷ 54 = 56

Next, multiply the resulting quotient by 19: 56 × 19 = 56 × (20 - 1) = 1120 - 56 = 1064

Finally, subtract 84 from the product to obtain the final value: 1064 - 84 = 980

Explanation

To evaluate the expression, calculate each percentage term on the left-hand side separately.

First percentage calculation: 30% of 1225 = (30 / 100) × 1225 = 0.30 × 1225 = 367.5

Second percentage calculation: 64% of 555 = (64 / 100) × 555 = 0.64 × 555 = 355.2

Subtract the second calculated value from the first: 367.5 - 355.2 = 12.3

Explanation

To calculate the average number of tourists traveling by Train across all cities, first sum the values listed under the Train column for each city: Delhi = 188 Mumbai = 166 Chandigarh = 194 Dehradun = 185 Mussoorie = 159 Jaipur = 163

Total tourists by Train = 188 + 166 + 194 + 185 + 159 + 163 = 1055

Calculate the average by dividing the total number of tourists by the total number of cities (6): Average = 1055 / 6 = 175.833... ≈ 175.83

Explanation

Total tourists visiting Mumbai across all modes of transport = 180 + 166 + 178 + 187 + 182 = 893. Total tourists visiting Mussoorie across all modes of transport = 149 + 159 + 155 + 149 + 183 = 795. Required difference = 893 - 795 = 98.

Explanation

Number of tourists visiting Dehradun by train = 185. Number of tourists visiting Chandigarh by air = 148. Percentage = (185 / 148) × 100 = 1.25 × 100 = 125%.

Explanation

Total tourists traveling by air = 174 + 182 + 148 + 148 + 183 + 174 = 1009. Average tourists by air = 1009 / 6 = 168.17. Total tourists traveling by bus = 172 + 178 + 163 + 142 + 155 + 158 = 968. Average tourists by bus = 968 / 6 = 161.33. Difference between the two averages = (1009 - 968) / 6 = 41 / 6 ≈ 6.83.

Explanation

Number of tourists traveling to Delhi by car = 192. Number of tourists traveling to Mumbai by air = 182. Required ratio = 192 : 182 = (192 / 2) : (182 / 2) = 96 : 91.

Explanation

Distance covered = 1.1 km = 110000 cm. Distance covered in N revolutions = N × 2 × π × r. 560 × 2 × (22 / 7) × r = 110000 3520 × r = 110000 r = 110000 / 3520 = 31.25 cm.

Explanation

Let Elena's present age be x years. According to the given condition, x + 15 = 5 × (x - 5). Expanding and solving for x: x + 15 = 5x - 25 4x = 40 x = 10 years.

Explanation

Present worth (PW) of ₹3600 due 2 years hence at 10% per annum simple interest is given by PW = S / (1 + (r × t) / 100). PW = 3600 / (1 + (10 × 2) / 100) = 3600 / 1.2 = ₹3000. Since the purchase price is ₹3000 and the present worth of the selling price is ₹3000, the effective gain is 0%.

Explanation

Downstream speed = Distance / Time = 15 km / 3.75 hours = 4 km/h. Upstream speed = Distance / Time = 5 km / 2.5 hours = 2 km/h. Speed of the stream = (Downstream speed - Upstream speed) / 2 = (4 - 2) / 2 = 1 km/h.

Explanation

Area of wet surface = Base area + 2 × Height × (Length + Width) Length = 6 m, Width = 4 m, Height = 1.25 m. Base area = 6 × 4 = 24 m². Area of 4 wet side walls = 2 × 1.25 × (6 + 4) = 2.5 × 10 = 25 m². Total wet surface area = 24 + 25 = 49 m².

Explanation

Profit percentage = (Profit / Cost Price) × 100. For a cost price of 60 and profit of 29, the profit percentage is (29 / 60) × 100 = 48.33%, which is higher than the percentage profit of any other listed transaction.

Explanation

Milk proportion in Vessel A = 4/7 Milk proportion in Vessel B = 2/5 Desired milk proportion in Mixture C = 1/2

By the rule of alligation: Ratio of Vessel A to Vessel B = (1/2 - 2/5) : (4/7 - 1/2) = (1/10) : (1/14) = 14 : 10 = 7 : 5.