IBPS RRB Clerk Prelims 2016 Numerical Ability Questions with Solutions

Explanation

Using the successive percentage change formula: Net percentage increase = a + b + (a × b) / 100 Substituting a = 5 and b = 20: Net increase = 5 + 20 + (5 × 20) / 100 = 25 + 1 = 26%

Explanation

In 140 litres of mixture, milk constitutes 90%, which is 126 litres. When 30 litres of mixture is removed, the milk removed is 90% of 30 = 27 litres. Remaining milk in the jar = 126 - 27 = 99 litres. Adding x litres of milk makes the total milk 112 litres: 99 + x = 112 x = 13 litres

Explanation

75% of 160 = (3 / 4) × 160 = 120 40% of y% of 600 = (40 / 100) × (y / 100) × 600 = 2.4y 2.4y = 120 y = 120 / 2.4 = 50

Explanation

Side of the square = √256 = 16 metres. Breadth of the rectangle (b) = 16 metres. Since the difference between length and breadth is 2 metres, length (l) = 16 + 2 = 18 metres. Area of the rectangle = l × b = 18 × 16 = 288 square metres.

Explanation

Let the monthly salary be S. Mutual fund investment = 50% of S = 0.50S. Remaining salary = 50% of S = 0.50S. The ratio of expenditure on rent and groceries is 3 : 2, so grocery expenditure = (2 / 5) × 0.50S = 0.20S. 0.20S = 18,000 S = 90,000 Mutual fund investment = 0.50 × 90,000 = Rs. 45,000.

Explanation

Amount A = P(1 + R / 100)² 1296 = 900(1 + R / 100)² (1 + R / 100)² = 1296 / 900 = 1.44 1 + R / 100 = √1.44 = 1.2 R / 100 = 0.2 R = 20% per annum

Explanation

Given equation: x / 8 = y / 12 + 3 Also, y = 120% of x = 1.2x = 6x / 5 Substitute y in the equation: x / 8 = (6x / 5) / 12 + 3 x / 8 = x / 10 + 3 x / 8 - x / 10 = 3 (5x - 4x) / 40 = 3 x / 40 = 3 x = 120

Explanation

Profit on article A = 30% of 270 = Rs. 81 Profit on article B = 40% of 270 = Rs. 108 Total profit = 81 + 108 = Rs. 189

Explanation

Total purchases of magazines P and R in January = 55 + 54 = 109. Total purchases of magazines P and R in March = 56 + 42 = 98. Difference = 109 - 98 = 11.

Explanation

Total people who purchased magazine P in May = 65. Number of females = 39. Number of males = 65 - 39 = 26. Ratio of males to females = 26 : 39 = 2 : 3.

Explanation

To find the average number of people who purchased magazine S in January, March, and April, sum the values for these months and divide by 3:

Average = (57 + 45 + 57) / 3 = 159 / 3 = 53

Explanation

Sum the number of purchasers for magazine Q in February and April: 60 + 80 = 140. Next, sum the number of purchasers for magazine R in February and April: 75 + 75 = 150. The required ratio is 140 : 150, which simplifies to 14 : 15.

Explanation

The percentage is given by dividing the number of purchasers of magazine R in March by the number of purchasers of magazine R in January, then multiplying by 100:

Percentage = (42 / 54) × 100 = (7 / 9) × 100 = 77.78%

Rounding to the nearest whole number gives 78%.

Explanation

First, perform the subtraction on the left side of the equation:

6840 - 1820 = 5020

Then, solve for the unknown value by subtracting 3750 from 5020:

? = 5020 - 3750 = 1270

Explanation

Convert the mixed numbers into improper fractions and simplify:

5½ + 3¾ = 11/2 + 15/4 = 22/4 + 15/4 = 37/4

To find the missing value, subtract 37/4 from 12:

? = 12 - 37/4 = 48/4 - 37/4 = 11/4 = 2¾

Explanation

Following BODMAS rules, division and multiplication are evaluated from left to right: 62 ÷ 12 × 4 = (62 / 12) × 4 = (31 / 6) × 4 = 124 / 6 = 62 / 3 = 20 ⅔

Explanation

First, calculate the product on the right side of the equation:

45 × 40 = 1800

Then, isolate the missing value by subtracting 1580 from 1800:

? = 1800 - 1580 = 220

Explanation

First, evaluate the sum inside the parentheses:

1330 + 1220 = 2550

Next, solve for the unknown divisor:

? = 2550 / 212.5 = 12

Explanation

First, calculate the difference inside the parentheses:

460 - 340 = 120

Then, calculate 60% of 120:

(60 / 100) × 120 = 0.6 × 120 = 72

Explanation

Evaluating the terms separately according to BODMAS rules: First term: 1200 ÷ (4 / 3) = 1200 × (3 / 4) = 900 Second term: 800 × 1.1 = 880

Subtracting the second term from the first: 900 - 880 = 20

Explanation

Evaluating the left-hand side of the equation: 625 × (1 / 25) × 4 = 25 × 4 = 100

Setting up the equation with the missing value: 100 = 20 × ? ? = 100 / 20 = 5

Explanation

To find the required value, evaluate the given fraction of fraction expression: (5 / 8) × (4 / 15) × 372

Simplifying the product of the fractions first: (5 × 4) / (8 × 15) = 20 / 120 = 1 / 6

Now multiply by 372: (1 / 6) × 372 = 62

Explanation

First calculate 20% of 220: (20 / 100) × 220 = 0.20 × 220 = 44

Substitute this into the original equation: 44 × ? = 35.2

Solving for the question mark: ? = 35.2 / 44 = 0.8

Explanation

Rewrite the given expression to identify the standard algebraic formula: 8.7 × 8.7 - 3.4 × 8.7 + 1.7 × 1.7 = (8.7)² - 2 × (1.7) × (8.7) + (1.7)²

This fits the algebraic identity a² - 2ab + b² = (a - b)², where a = 8.7 and b = 1.7.

Substituting these values into the formula: (8.7 - 1.7)² = (7)² = 49

Explanation

Perform the arithmetic operations in sequence from left to right:

First, add the positive terms: 189.25 + 329.95 = 519.20

Next, subtract 444.2 from the result: 519.20 - 444.20 = 75

Explanation

According to the BODMAS rule, division must be performed before subtraction.

First, divide 152 by 8: 152 ÷ 8 = 19

Next, subtract 19 from 278: 278 - 19 = 259

Explanation

According to the BODMAS rule, perform the multiplication step on the left-hand side first: 0.8 × 1.5 = 1.2

Subtract this from 3.6 to simplify the left-hand side: 3.6 - 1.2 = 2.4

Now solve the resulting equation: 2.4 = 5 - ? ? = 5 - 2.4 = 2.6

Explanation

Analyze the differences between consecutive terms in the series: 6 - 5 = 1 24 - 6 = 18 58 - 24 = 34 107 - 58 = 49

Now analyze the second differences between these consecutive first differences: 18 - 1 = 17 34 - 18 = 16 49 - 34 = 15

The second differences decrease by 1 at each step (17, 16, 15, ...). Thus, the next second difference is 14.

The next first difference is: 49 + 14 = 63

Adding this difference to the last term of the series gives: 107 + 63 = 170

Explanation

Analyze the relationship between consecutive terms in the given series starting from right to left: 13 × 2 = 26 26 × 2 = 52 52 × 2 = 104

Moving from left to right, each term is obtained by dividing the preceding term by 2: 104 ÷ 2 = 52 52 ÷ 2 = 26 26 ÷ 2 = 13

Applying this pattern to the start of the series: ? = 416 ÷ 2 = 208 208 ÷ 2 = 104

Explanation

Analyze the differences between consecutive terms in the decreasing series: 452 - 440 = 12 440 - 416 = 24 416 - 368 = 48 368 - 272 = 96

The differences form a geometric progression where each term is twice the previous difference (12, 24, 48, 96).

The next difference in the sequence is: 96 × 2 = 192

Subtracting this difference from the previous term yields: 272 - 192 = 80

Explanation

The logic of the number series is multiplication by successive natural numbers: 13 × 1 = 13 13 × 2 = 26 26 × 3 = 78 78 × 4 = 312 312 × 5 = 1560

Explanation

The differences between consecutive terms follow the pattern of squares of consecutive odd numbers: 17 - 8 = 9 = 3² 42 - 17 = 25 = 5² 91 - 42 = 49 = 7² 172 - 91 = 81 = 9² The next difference is 11² = 121. Required term = 172 + 121 = 293

Explanation

The differences between consecutive terms are perfect cubes: 8 - 7 = 1 = 1³ 16 - 8 = 8 = 2³ 43 - 16 = 27 = 3³ 107 - 43 = 64 = 4³ The next difference is 5³ = 125. Required term = 107 + 125 = 232

Explanation

Total time taken initially is 1 hour 12 minutes, which equals 72 minutes. Since speed is constant, distance is directly proportional to time: Distance = (150 / 72) × 108 = 150 × 1.5 = 225 km

Explanation

Using the simple interest formula SI = (P × R × T) / 100: 364 = (x × 14 × 2) / 100 364 = 28x / 100 x = (364 × 100) / 28 = 1300

The new principal is x + 100 = 1300 + 100 = 1400. Interest on Rs. 1400 at 14% per annum for 3 years: SI = (1400 × 14 × 3) / 100 = 14 × 42 = 588

Explanation

Work done by A in 1 day = 1/54 Work done by B in 1 day = 1/45 Combined 1-day work = 1/54 + 1/45 = (5 + 6) / 270 = 11/270 Fraction of work completed in 9 days = 9 × (11/270) = 11/30

Explanation

Let the present ages of A and B be 5x and 6x. Given that A is 7 years younger than B: 6x - 5x = 7 x = 7

Present age of A = 5 × 7 = 35 years Present age of B = 6 × 7 = 42 years

After 14 years: A's age = 35 + 14 = 49 years B's age = 42 + 14 = 56 years Respective ratio = 49 : 56 = 7 : 8

Explanation

Area of circle A = π × (r_A)² = 616 (22 / 7) × (r_A)² = 616 (r_A)² = (616 × 7) / 22 = 196 r_A = 14 cm

Radius of circle B = r_A + 14 = 14 + 14 = 28 cm

Explanation

Upstream time = 4 hours 30 minutes = 4.5 hours Upstream speed = Distance / Time = 90 / 4.5 = 20 km/h

Let boat speed in still water be b km/h and current speed be v = 6 km/h. Upstream speed = b - v = 20 b - 6 = 20 b = 26 km/h

Downstream speed = b + v = 26 + 6 = 32 km/h

Explanation

Initial total score of 54 children = 54 × 72 = 3888 Total score of 6 new children = 6 × 76 = 456 New total score = 3888 + 456 = 4344 Total number of children = 54 + 6 = 60 New average score = 4344 / 60 = 72.4

Alternatively, using deviations: Extra score brought by 6 children = 6 × (76 - 72) = 24 Increase in average = 24 / 60 = 0.4 New average = 72 + 0.4 = 72.4

Explanation

Let the initial total mixture be M. Initial milk quantity is 0.80 M. When 75% of the mixture is removed, 25% remains. Milk remaining = 0.80 × 0.25 M = 0.20 M. Adding 10 units of water gives total volume = 0.25 M + 10. The new milk concentration is 60%: 0.20 M / (0.25 M + 10) = 0.60 0.20 M = 0.15 M + 6 0.05 M = 6 M = 120 Initial milk quantity = 0.80 × 120 = 96.

Explanation

Ratio of investments is A : B : C : D = 2 : 3 : 5 : 7. A and B invested for 12 months, while C and D invested for 8 months. Effective profit sharing ratio = (2 × 12) : (3 × 12) : (5 × 8) : (7 × 8) = 24 : 36 : 40 : 56 = 6 : 9 : 10 : 14. Let total profit parts be x. C's share corresponds to 10 parts, which equals Rs. 12000. 1 part = 12000 / 10 = Rs. 1200. Share of B = 9 parts = 9 × 1200 = Rs. 10800.

Explanation

Percentage change in area = a + b + (a × b) / 100 Substituting a = +49.99% and b = -10.01%: Net change = 49.99 - 10.01 - (49.99 × 10.01) / 100 = 39.98 - 5.004 = 34.976% Rounding to the nearest whole percentage gives a 35% increase.

Explanation

Simple Interest = (P × R × T) / 100 Interest from Scheme 1 = (6000 × x × 6) / 100 = 360x Interest from Scheme 2 = (6000 × (x + 2) × 4) / 100 = 240(x + 2) = 240x + 480 Given difference = 720: 360x - (240x + 480) = 720 120x - 480 = 720 120x = 1200 x = 10%

Explanation

Total Cost Price = (150 × 250) + 2500 = 37500 + 2500 = Rs. 40000. Selling Price per calculator = 320 × (1 - 0.05) = Rs. 304. Total Selling Price = 150 × 304 = Rs. 45600. Profit Percentage = [(45600 - 40000) / 40000] × 100 = (5600 / 40000) × 100 = 14%.

Explanation

Sum of weights of A, B, C = 3 × 84 = 252 kg. Sum of weights of A, B, C, D = 4 × 80 = 320 kg. Weight of D = 320 - 252 = 68 kg. Weight of E = 68 + 3 = 71 kg. Sum of weights of B, C, D, E = 4 × 79 = 316 kg. Replacing (B + C + D) with (320 - A): (320 - A) + 71 = 316 391 - A = 316 A = 75 kg.

Explanation

Retailer's Cost Price = Selling Price / (1 + Profit Rate) = 1955 / 1.15 = Rs. 1700. Wholesale List Price = Retailer's Cost Price / (1 - Discount Rate) = 1700 / (1 - 0.15) = 1700 / 0.85 = Rs. 2000. Discount received from wholesaler = Wholesale List Price - Retailer's Cost Price = 2000 - 1700 = Rs. 300.

Explanation

Initial weight of low quality wheat in 150 kg = 10% of 150 = 15 kg. Let x kg of good quality wheat be added. Total weight of mixture = 150 + x. Percentage of low quality wheat = [15 / (150 + x)] × 100 = 5% 15 / (150 + x) = 1 / 20 300 = 150 + x x = 150 kg.

Explanation

Total balls = 6 + 4 + 2 = 12. Total sample space outcomes = 12C3 = (12 × 11 × 10) / (3 × 2 × 1) = 220. Favorable outcomes for 3 balls of same color: 3 red balls = 6C3 = 20 3 blue balls = 4C3 = 4 3 green balls = 2C3 = 0 Total favorable outcomes = 20 + 4 = 24. Probability = 24 / 220 = 6 / 55.

Explanation

Let the initial height of each candle be 1 unit. Burning rate of first candle = 1/5 per hour. Burning rate of second candle = 1/4 per hour. After t hours, height of first candle = 1 - t/5 = (5 - t)/5. Height of second candle = 1 - t/4 = (4 - t)/4. Equating the ratio of heights to 3/2: [(5 - t)/5] / [(4 - t)/4] = 3 / 2 [4(5 - t)] / [5(4 - t)] = 3 / 2 8(5 - t) = 15(4 - t) 40 - 8t = 60 - 15t 7t = 20 t = 20 / 7 hours.