SSC CHSL Tier 1 2021 Quantitative Aptitude Questions with Solutions

Explanation

Let the weight of the rice costing ₹47.50 per kg be x kg. The weight of the rice costing ₹40 per kg is 15 - x kg.

The total cost of the blended rice is ₹645, which gives the equation: 40(15 - x) + 47.5x = 645

Solving for x: 600 - 40x + 47.5x = 645 7.5x = 45 x = 6

Explanation

Using the formula for average, the total sum is equal to the average multiplied by the number of observations.

For the group of 10 students, the total marks X is: X = 10 × A

For the group of 15 students, the total marks Y is: Y = 15 × (A + 8)

The ratio of their total marks is given as X:Y = 3:5. Substituting the expressions for X and Y into this ratio: (10 × A) / (15 × (A + 8)) = 3/5

Simplifying the fraction on the left side: (2A) / (3(A + 8)) = 3/5

Cross-multiplying to solve for A: 2A × 5 = 3 × 3(A + 8) 10A = 9(A + 8) 10A = 9A + 72 A = 72

Now, substitute the value of A to find X and Y: X = 10 × 72 = 720 Y = 15 × (72 + 8) = 15 × 80 = 1200

The required value is A + X + Y: A + X + Y = 72 + 720 + 1200 = 1992

Explanation

The first train starts at 9:00 a.m. and travels at 240 km/h. The second train starts 30 minutes (½ hour) later at 9:30 a.m. and travels at 300 km/h.

During the ½ hour before the second train starts, the first train covers a distance of: 240 km/h × ½ h = 120 km

The relative speed of the second train with respect to the first train is: 300 km/h - 240 km/h = 60 km/h

The time taken by the second train to catch up to the first train is: 120 km ÷ 60 km/h = 2 hours

The distance from Agra where they meet is the distance covered by the second train in these 2 hours: 300 km/h × 2 h = 600 km

Explanation

Expand the left side of the given identity by multiplying the algebraic expressions:

4(z + 7)(2z - 1) = 4(2z² - z + 14z - 7) = 4(2z² + 13z - 7) = 8z² + 52z - 28

Comparing this with the right side of the identity, Az² + Bz + C, we equate the corresponding coefficients of the like terms:

A = 8 B = 52 C = -28

Now, substitute these values into the expression A² - B - C:

A² - B - C = 8² - 52 - (-28) = 64 - 52 + 28 = 12 + 28 = 40

Explanation

The total surface area (TSA) of a cylindrical container is calculated using the formula:

TSA = 2πr(h + r)

Here, the radius r is half of the diameter, so: r = 14 / 2 = 7 cm

The height h is given as 25 cm.

Substituting the given values into the formula:

TSA = 2 × (22 / 7) × 7 × (25 + 7) TSA = 2 × 22 × 32 TSA = 44 × 32 TSA = 1408 cm²

Explanation

To find the difference between the compound interest compounded yearly and half-yearly, we calculate the final amount in both scenarios.

For yearly compounding, the interest is calculated for 1 full year at 4% and for the remaining ½ year at 2%. Amount = P × (1 + R/100) × (1 + (R × ½)/100) Amount = 10000 × (1 + 4/100) × (1 + 2/100) Amount = 10000 × 1.04 × 1.02 = ₹ 10608

For half-yearly compounding, the rate is halved to 2% per half-year, and the time period is doubled to 3 half-years. Amount = P × (1 + R/100)³ Amount = 10000 × (1 + 2/100)³ Amount = 10000 × (1.02)³ Amount = 10000 × 1.061208 = ₹ 10612.08

The difference between the two amounts gives the difference in the compound interests: Difference = 10612.08 - 10608 = ₹ 4.08

Explanation

An average score of exactly 94% across 5 subjects, each out of 100, requires a total sum of marks equal to:

Total marks required = 94 × 5 = 470

Calculating the sum of marks secured by Cavin across all 5 subjects:

Cavin's total marks = 96 + 99 + 94 + 87 + 94 = 470

Dividing this total by the number of subjects gives the average:

Average = 470 / 5 = 94%

Explanation

For the first option of three successive discounts of 10% each, the final selling price is calculated using the successive multiplication formula:

Selling Price 1 = Marked Price × (1 - d/100)³ Selling Price 1 = 3000 × (1 - 10/100)³ = 3000 × (0.9)³ = 3000 × 0.729 = ₹2187

For the second option of a single discount of 30%, the final selling price is:

Selling Price 2 = Marked Price × (1 - d/100) Selling Price 2 = 3000 × (1 - 30/100) = 3000 × 0.7 = ₹2100

Comparing the two options, the difference in the amount paid by the buyer is:

2187 - 2100 = ₹87

Therefore, the buyer pays ₹87 extra in the former option compared to the second option.

Explanation

Let the total number of valid votes be V.

Since there are only two candidates, if one candidate gets 38% of the valid votes, the other candidate gets the remaining votes: 100% - 38% = 62% of V

The difference in votes between the winning candidate and the losing candidate is: 62% of V - 38% of V = 24% of V

This difference is given as 7200 votes: 24% of V = 7200

Solving for V: V × 24/100 = 7200 V = 7200 × 100 / 24 V = 300 × 100 V = 30000

Explanation

Correct Answer: B

To find the value of the expression x⁵ - 10x⁴ + 10x³ - 10x² + 10x - 1 when x = 9, we can substitute 10 with x + 1 since 9 + 1 = 10.

Replacing 10 with x + 1 in the expression: x⁵ - (x + 1)x⁴ + (x + 1)x³ - (x + 1)x² + (x + 1)x - 1

Expanding the terms: x⁵ - x⁵ - x⁴ + x⁴ + x³ - x³ - x² + x² + x - 1

All the higher-degree terms cancel each other out: (x⁵ - x⁵) + (-x⁴ + x⁴) + (x³ - x³) + (-x² + x²) + x - 1 = x - 1

Substituting x = 9 back into the simplified expression: 9 - 1 = 8

Explanation

For any two numbers a and b, if their third proportional is c, then the relationship is defined by the proportion a : b = b : c, which simplifies to the formula c = b² / a.

Given the numbers a = 42 and b = 63, we substitute these values into the formula:

c = 63² / 42 c = (63 × 63) / 42

Dividing 63 and 42 by their greatest common divisor, 21:

63 / 21 = 3 42 / 21 = 2

This simplifies the calculation to:

c = (3 × 63) / 2 c = 189 / 2 c = 94.5

Explanation

When a body travels equal distances at two different speeds, say x and y, the average speed for the entire journey is given by the harmonic mean formula:

Average Speed = 2xy / (x + y)

Here, the distance from city A to city B is equal to the return distance from city B to city A.

Given: Speed from A to B (x) = 24 km/h Speed from B to A (y) = 16 km/h

Substituting these values into the formula:

Average Speed = 2 × 24 × 16 / (24 + 16) Average Speed = 768 / 40 Average Speed = 19.2 km/h

Explanation

The total volume of the toy is the sum of the volumes of its three components: the cylinder, the cone, and the hemisphere. Representing the total volume of the toy as 100%, the cylinder contributes 50% and the cone contributes 20%.

The contribution of the hemisphere is the remaining percentage of the total volume: 100% - 50% - 20% = 30%

The ratio of the volume contributions of the cone, cylinder, and hemisphere in this specific order is: Cone : Cylinder : Hemisphere = 20% : 50% : 30% = 2 : 5 : 3

Explanation

Applying the BODMAS rule, which specifies the order of operations as Brackets, Orders (exponents), Division and Multiplication, and Addition and Subtraction:

First, evaluate the terms with exponents: 3³ = 27 2² = 4

Next, simplify the terms inside the brackets: (28 - 3³) = 28 - 27 = 1 [(28 - 3³) + 99] = 1 + 99 = 100 (44 - 2²) = 44 - 4 = 40

Substitute these simplified values back into the main expression: 100 + 136 ÷ 4 × 5 - 40

Now perform division and multiplication from left to right: 136 ÷ 4 = 34 34 × 5 = 170

Finally, perform the addition and subtraction from left to right: 100 + 170 - 40 = 270 - 40 = 230

Explanation

The longest stick that can be placed inside a cubical vessel of edge length a corresponds to the body diagonal of the cube.

The formula for the length of the body diagonal of a cube is: d = a√3

Substituting the given edge length a = 20 cm into this relation yields: d = 20√3 cm

Explanation

Using the average deviation formula, the score in the nth inning that increases the average is: Score in nth inning = New Average + (Previous number of innings × Increase in average)

Here, the new average after 17 innings is 37, which represents an increase of 9 runs. The previous number of innings is 16.

Substituting these values into the formula: Score in 17th inning = 37 + (16 × 9) Score in 17th inning = 37 + 144 Score in 17th inning = 181

Alternatively, using total runs: Total runs in 17 innings = 17 × 37 = 629 Since the average increased by 9 runs, the average of the first 16 innings was 37 - 9 = 28. Total runs in 16 innings = 16 × 28 = 448 Runs in the 17th inning = 629 - 448 = 181

Explanation

By the rule of allegation, the ratio of the number of officers to the number of workers is inversely proportional to the differences between their respective average salaries and the combined average salary.

Let O be the number of officers and W be the number of workers. Let the combined average monthly salary of all employees be S.

The average monthly salary of an officer is S + 78000, so the difference between the officer average and the combined average is 78000.

The average monthly salary of a worker is S - 42000, so the difference between the combined average and the worker average is 42000.

Using the weighted average relation: O × (S_officer - S) = W × (S - S_worker)

Substituting the values gives: O × 78000 = W × 42000

This simplifies to: O / W = 42000 / 78000 = 7 / 13

The total number of employees is represented by O + W = 7 + 13 = 20 units.

The percentage of officers among all employees is: (O / (O + W)) × 100% = (7 / 20) × 100% = 35%

Explanation

The expression 1/sin α is equivalent to csc α. For any acute angle α, csc α is equal to sec α if and only if α = 45°. For all other acute angles, the two values differ. For example, if α = 30°, sec 30° = 2/√3 ≈ 1.15, while 1/sin 30° = 2. Therefore, 1/sin α is not necessarily equal to sec α.

Explanation

The circumference of the base of a cylinder is given by the formula C = 2πr, where r is the radius of the base.

Given that the circumference is 4π cm: 2πr = 4π r = 2 cm

The curved surface area of a cylinder is given by the formula CSA = 2πrh, where h is the height.

Given that the curved surface area is 12π cm²: 2πrh = 12π Substituting r = 2 cm: 2π × 2 × h = 12π 4πh = 12π h = 3 cm

The volume of a cylinder is given by the formula V = πr²h.

Substituting the values of r and h: V = π × 2² × 3 V = π × 4 × 3 V = 12π cm³

Explanation

The curved surface area of a right circular cone is given by the formula: Curved Surface Area = π × r × l

where r is the radius of the base and l is the slant height of the cone.

Given that the radius r is 28 cm, the curved surface area is 4664 cm², and π is 22/7, we substitute these values into the formula: 4664 = (22/7) × 28 × l

Simplifying the expression: 4664 = 22 × 4 × l 4664 = 88 × l

Solving for the slant height l: l = 4664 / 88 l = 53 cm

Explanation

The percentage increase is calculated using the formula:

Percentage Increase = ((New Value - Original Value) / Original Value) × 100%

Substituting the given values into the formula: Original Value = 36 New Value = 63

Absolute Increase = 63 - 36 = 27

Percentage Increase = (27 / 36) × 100% = 3/4 × 100% = 75%

Explanation

For two numbers a and b, their third proportional c is defined by the relation a : b = b : c, which simplifies to the formula:

c = b² / a

Substituting the given values, a = 16 and b = 24:

c = 24² / 16 c = 576 / 16 c = 36

Explanation

Let x = a - 15 and y = b - 10.

We need to find the value of x³ + y³. First, we calculate the sum of x and y: x + y = (a - 15) + (b - 10) x + y = a + b - 25

We are given that a + b = 25. Substituting this into the equation: x + y = 25 - 25 = 0

According to the algebraic identity, when x + y = 0, the sum of their cubes is also zero: x³ + y³ = (x + y)(x² - xy + y²) x³ + y³ = 0 × (x² - xy + y²) = 0

Therefore, substituting back the expressions for x and y: (a - 15)³ + (b - 10)³ = 0

Explanation

To find the value of p² + 2p, we first solve the given equation: p³ + 3p² + 3p = 26

By adding 1 to both sides of the equation, we can complete the cube on the left-hand side using the algebraic identity (a + b)³ = a³ + 3a²b + 3ab² + b³: p³ + 3p² + 3p + 1 = 26 + 1 (p + 1)³ = 27

Taking the cube root of both sides gives: p + 1 = 3 p = 2

Now, substitute the value of p = 2 into the required expression: p² + 2p = 2² + 2(2) = 4 + 4 = 8

Explanation

By the exterior angle theorem, the exterior angle of a triangle is equal to the sum of its two opposite interior angles. Here, when side CA of triangle ABC is produced to P, the exterior angle ∠BAP is equal to the sum of the interior angles ∠B and ∠C:

∠B + ∠C = ∠BAP = 126°

The ratio of the angles is given as ∠B : ∠C = 5 : 2. Let ∠B = 5x and ∠C = 2x.

Substituting these values into the sum: 5x + 2x = 126° 7x = 126° x = 18°

Now, calculating the individual angle measures: ∠B = 5 × 18° = 90° ∠C = 2 × 18° = 36°

Explanation

Correct Answer: A

The net percentage change in sales when two successive percentage changes x and y occur is given by the formula:

Net change % = x + y + xy/100

Here, the price is reduced by 20%, so x = -20%. The quantity sold is increased by 40%, so y = +40%.

Substituting these values into the formula:

Net change % = -20 + 40 + (-20 × 40)/100 Net change % = 20 - 800/100 Net change % = 20 - 8 Net change % = 12%

Since the resulting value is positive, there is a 12% increase in overall sales.

Explanation

Let the terms in the expression be represented by a = 5 ½ and b = 2 ¾.

Converting these mixed fractions into improper fractions: a = 11/2 b = 11/4

The given expression is (a² - b²) ÷ b, which can be expanded as: a²/b - b

Substituting the values of a and b into the first term: a²/b = (11/2)² ÷ (11/4) = (121/4) × (4/11) = 11

Subtracting b from this result: 11 - 11/4 = (44 - 11)/4 = 33/4

Converting 33/4 back into a mixed fraction: 33/4 = 8 ¼

Explanation

Relative speed when two objects move in the same direction is the difference of their individual speeds.

Relative speed = Speed of Neha - Speed of Malay Relative speed = 11 rounds/hour - 7 rounds/hour = 4 rounds/hour

They start from the same point and in the same direction, so they will first cross each other when the relative distance covered between them equals 1 full round of the circular field.

Time taken to cross each other = Relative distance / Relative speed Time taken = 1 round / 4 rounds/hour = ¼ hour

Converting hours into minutes: ¼ × 60 minutes = 15 minutes

Since they started at 02:45 p.m., they will first cross each other 15 minutes later: 02:45 p.m. + 15 minutes = 03:00 p.m.

Explanation

For the number 5X8146Y to be divisible by 88, it must be divisible by both 8 and 11, as 8 and 11 are co-prime factors of 88.

According to the divisibility rule of 8, the number formed by the last three digits of 5X8146Y must be divisible by 8. These digits are 46Y. Dividing 460 by 8 leaves a remainder of 4, so the next multiple of 8 is 464. Thus, the value of Y must be 4.

With Y = 4, the number becomes 5X81464.

According to the divisibility rule of 11, the difference between the sum of the digits at odd positions and the sum of the digits at even positions must be 0 or a multiple of 11.

Sum of digits at odd positions starting from the right: 4 + 4 + 8 + 5 = 21 Sum of digits at even positions starting from the right: 6 + 1 + X = 7 + X

Difference = 21 - (7 + X) = 14 - X

For this difference to be a multiple of 11, the expression 14 - X must equal 11. This gives X = 3.

Explanation

We can solve this efficiently using the weighted average formula for profit/loss percentage:

Overall Profit % = (w₁ × P₁ + w₂ × P₂) / (w₁ + w₂)

Let the total land be divided into 5 equal parts. The weight of the first portion is w₁ = 2, sold at a profit of P₁ = -10% (loss). The weight of the remaining portion is w₂ = 3, sold at a profit of P₂ = x%. The overall profit is 42%.

Substituting these values: 42 = (2 × (-10) + 3 × x) / 5 210 = -20 + 3x 3x = 230 x = 230/3 ≈ 76.7%

Explanation

The difference in distance covered in the two scenarios is equal to the difference in the lengths of the two platforms.

Difference in distance = 600 - 400 = 200 m Difference in time = 60 - 50 = 10 s

Speed of the train v = Distance / Time = 200 / 10 = 20 m/s

Converting the speed to km/h: v = 20 × 18/5 = 72 km/h

Let the length of the train be L. When crossing a platform, the total distance covered is the sum of the train's length and the platform's length. Using the relation for the first platform: L + 400 = Speed × Time L + 400 = 20 × 50 L + 400 = 1000 L = 600 m

This gives a train length of 600 m and a speed of 72 km/h.

Explanation

We are given the equation: a/b + b/a = -1

Taking the common denominator on the left-hand side: (a² + b²) / ab = -1

Multiplying both sides by ab: a² + b² = -ab

Rearranging the terms gives: a² + ab + b² = 0

We need to find the value of 6(a³ - b³). Using the standard algebraic identity for the difference of cubes: a³ - b³ = (a - b)(a² + ab + b²)

Substituting the relation a² + ab + b² = 0 into the identity: a³ - b³ = (a - b) × 0 = 0

Multiplying by 6: 6(a³ - b³) = 6 × 0 = 0

Explanation

Correct Answer: B

The curved surface area of a hemisphere is given by the formula: CSA = 2πr²

Substituting the given values into the formula: 1232 = 2 × (22/7) × r² 1232 = (44/7) × r² r² = (1232 × 7) / 44 r² = 28 × 7 r² = 196 r = √196 r = 14 cm

Explanation

The population compound growth formula is: A = P × (1 + r/100)ⁿ

Here: A is the present population = 93051 P is the population 2 years ago r is the annual growth rate = 5% n is the number of years = 2

Substituting these values into the formula: 93051 = P × (1 + 5/100)² 93051 = P × (21/20)² 93051 = P × (441/400)

Rearranging the equation to solve for P: P = 93051 × 400 ÷ 441 P = 211 × 400 P = 84400

Explanation

Let the total work be the least common multiple of 6 and 9, which is 18 units.

Asha's rate of work is 18 / 6 = 3 units per day. Bhuvan's rate of work is 18 / 9 = 2 units per day.

They work on alternate days, starting with Asha. In one complete 2-day cycle, the total work done by both is 3 + 2 = 5 units.

To find the number of full cycles, we divide the total work by the work done in one cycle: 18 / 5 = 3 cycles with a remainder of 3 units.

The time taken for 3 complete cycles is 3 × 2 = 6 days, during which 15 units of work are completed.

The remaining work is 18 - 15 = 3 units. On the 7th day, it is Asha's turn to work. Since her rate is 3 units per day, she will complete the remaining 3 units of work in exactly 1 day.

Thus, the total time taken to complete the entire work is 6 + 1 = 7 days.

Explanation

The sum of all interior angles in a triangle is always 180°. Let the three angles of the triangle be 3x, 4x, and 8x.

3x + 4x + 8x = 180° 15x = 180° x = 12°

The measure of the smallest angle is 3x: 3 × 12° = 36°

Explanation

The mean of grouped data is calculated using the formula:

Mean = ∑(f × x) / ∑f

where x represents the mid-point of each class interval and f represents the corresponding frequency.

The mid-points (x) and the products of frequency and mid-point (f × x) for each interval are:

For 0-10: mid-point x = 5, f × x = 2 × 5 = 10 For 10-20: mid-point x = 15, f × x = 11 × 15 = 165 For 20-30: mid-point x = 25, f × x = 28 × 25 = 700 For 30-40: mid-point x = 35, f × x = 6 × 35 = 210 For 40-50: mid-point x = 45, f × x = 3 × 45 = 135

Summing these values: Total frequency (∑f) = 2 + 11 + 28 + 6 + 3 = 50 Total sum of products (∑fx) = 10 + 165 + 700 + 210 + 135 = 1220

Applying the mean formula: Mean = 1220 / 50 = 24.4

Explanation

Given the trigonometric equation: sin x - 3 cos x = √3 cos x

To find the value of cot x, we divide the entire equation by sin x: 1 - 3 cot x = √3 cot x

Rearranging the terms to isolate cot x on one side: 1 = (3 + √3) cot x

Solving for cot x gives: cot x = 1 / (3 + √3)

To simplify, we multiply the numerator and the denominator by the conjugate of the denominator, which is 3 - √3: cot x = (3 - √3) / ((3 + √3)(3 - √3)) cot x = (3 - √3) / (3² - (√3)²) cot x = (3 - √3) / (9 - 3) cot x = (3 - √3) / 6

Explanation

The marked price of the refrigerator is £60,000.

The flat discount offered on full cash payment is £12,000.

The extra discount for regular customers is 5% of the marked price: 5% of £60,000 = (5 / 100) × 60,000 = £3,000

The total discount received by a regular customer paying in cash is the sum of both discounts: Total discount = £12,000 + £3,000 = £15,000

The final amount paid by the regular customer is the marked price minus the total discount: Amount paid = £60,000 - £15,000 = £45,000

Explanation

Let Soham's initial expenditure and savings be 5x and x respectively.

His initial income is the sum of his initial expenditure and savings: Initial Income = 5x + x = 6x

His income increases by 25%: New Income = 1.25 × 6x = 7.5x

His savings increase by 20%: New Savings = 1.20 × x = 1.2x

His current expenditure is the difference between his new income and new savings: Current Expenditure = 7.5x - 1.2x = 6.3x

Given that his current expenditure is £4,347: 6.3x = 4347 x = 4347 / 6.3 = 690

Soham's initial income is: 6x = 6 × 690 = 4140

Explanation

Correct Answer: B

The relationship between Marked Price (MP) and Cost Price (CP) is given by the formula:

MP/CP = (100 + Profit%) / (100 - Discount%)

Using the values from the first case:

MP/CP = (100 + 25) / (100 - 25) = 125/75 = 5/3

Let the profit percentage in the second case be P when the discount is 35%:

5/3 = (100 + P) / (100 - 35)

5/3 = (100 + P) / 65

100 + P = (5 × 65) / 3 = 325/3 ≈ 108.33

P ≈ 8.33%

Rounding to the nearest whole number, the profit percentage is 8%.

Explanation

According to the divisibility rule for 8, the remainder of a number when divided by 8 is determined solely by its last three digits. This is because any number can be expressed in the form 1000a + b, where b represents the last three digits, and 1000 is always divisible by 8.

For the number 8127, the last three digits are 127. Dividing 127 by 8 yields:

127 = 8 × 15 + 7

Since 120 is the largest multiple of 8 less than 127, the remainder is 7. Thus, dividing 8127 by 8 leaves a remainder of 7.

Explanation

The curved surface area of a cylinder is given by the formula:

Curved Surface Area = 2πrh

where r is the base radius and h is the height.

Substituting the given values, r = 2 cm, h = 6 cm, and π = 3.14, into the formula:

Curved Surface Area = 2 × 3.14 × 2 × 6 Curved Surface Area = 24 × 3.14 Curved Surface Area = 75.36 cm²

Explanation

To find the percentage of registered voters at Centre Q who cast invalid votes, first calculate the total votes cast at Centre Q:

Total votes cast at Q = 1850 × 80% = 1480

Given that the invalid votes at Centre Q represent 25% of the total votes cast at this centre:

Invalid votes at Q = 1480 × 25% = 370

Now, calculate the percentage of total registered voters at Centre Q who cast invalid votes:

Percentage = (370 / 1850) × 100 = 20%

Explanation

The given equation is: p⁴ + 1/p⁴ = 4354

By adding 2 on both sides to complete the square: p⁴ + 2 + 1/p⁴ = 4354 + 2 (p² + 1/p²)² = 4356 p² + 1/p² = 66

Now, subtracting 2 from both sides to form a perfect square for subtraction: p² - 2 + 1/p² = 66 - 2 (p - 1/p)² = 64 p - 1/p = 8

Using the algebraic identity for cubes: p³ - 1/p³ = (p - 1/p)³ + 3(p - 1/p)

Substituting p - 1/p = 8: p³ - 1/p³ = 8³ + 3(8) p³ - 1/p³ = 512 + 24 p³ - 1/p³ = 536

Explanation

Average speed is calculated as the ratio of the total distance traveled to the total time taken.

Total distance = 75 km + 45 km = 120 km

Time taken for the first part of the journey = 75 / 45 = 5/3 hours

Time taken for the second part of the journey = 45 / 70 = 9/14 hours

Total time = 5/3 + 9/14 = (70 + 27) / 42 = 97/42 hours

Average speed = Total distance / Total time = 120 / (97/42) = (120 × 42) / 97 = 5040 / 97 ≈ 51.96 km/h, which is approximately 51.93 km/h.

Explanation

According to the BODMAS rule, operations are performed in the order of Brackets, Of, Division, Multiplication, Addition, and Subtraction.

First, evaluate the innermost parentheses (9 of 3 + 6 - 4 × 7). Solve the of operation: 9 of 3 = 27 Perform multiplication: 4 × 7 = 28 Substitute these back: 27 + 6 - 28 = 33 - 28 = 5

Next, solve the middle parentheses using this result: 7 + 4 - 5 = 11 - 5 = 6

Substitute this result into the square brackets: 16 - 6 = 10

Finally, complete the addition outside the brackets: 8 + 10 = 18

Explanation

To find the combined ratio a:b:c, the term corresponding to b must be made equal in both given ratios.

The given ratios are: a:b = 2:3 b:c = 6:8

Multiply the first ratio by 2 to make the term for b equal to 6: a:b = (2 × 2) : (3 × 2) = 4:6

Now that the b term is 6 in both ratios, they can be combined directly: a:b:c = 4:6:8

Simplifying this ratio by dividing each term by 2 gives: a:b:c = 2:3:4

Explanation

By the rule of alligation, the ratio in which the two varieties of pulses must be mixed is:

Ratio = (Dearer price - Mean price) / (Mean price - Cheaper price)

Given: Cheaper price = ₹15 per kg Dearer price = ₹20 per kg Mean price = ₹18 per kg

Substituting these values into the formula:

Ratio = (20 - 18) / (18 - 15) = 2/3

Explanation

The average of the first n natural numbers is given by the formula:

Average = (n + 1) / 2

Substituting the value n = 43 into the formula:

Average = (43 + 1) / 2 = 44 / 2 = 22.