Answer: Option B. -> 39%

To calculate the average marks in mathematics of the class, we will use the weighted average method.
Weighted Average = (weight1 × value1) + (weight2 × value2) + (weight3 × value3)……
Weighted Average = (Total weight × Total value)

Let us consider the following data:
Division 1: Number of students = 30 and Average marks in mathematics = 40%
Division 2: Number of students = 40 and Average marks in mathematics = 30%
Division 3: Number of students = 30 and Average marks in mathematics = 50%

Total number of students = 30 + 40 + 30 = 100

We will calculate the total weight and total value of the class using the following formula:

Total Weight = (Number of students in Division 1 × Average marks in mathematics of Division 1) + (Number of students in Division 2 × Average marks in mathematics of Division 2) + (Number of students in Division 3 × Average marks in mathematics of Division 3)
Total Weight = (30 × 40) + (40 × 30) + (30 × 50)
Total Weight = 1200

Total Value = (Average marks in mathematics of Division 1 × Number of students in Division 1) + (Average marks in mathematics of Division 2 × Number of students in Division 2) + (Average marks in mathematics of Division 3 × Number of students in Division 3)
Total Value = (40 × 30) + (30 × 40) + (50 × 30)
Total Value = 1500

Now, we will calculate the average marks in mathematics of the class using the weighted average formula:
Weighted Average = (Total weight × Total value)
Weighted Average = (1200 × 1500)
Weighted Average = 1800000

Average marks in mathematics of the class = (Weighted Average ÷ Total number of students)
Average marks in mathematics of the class = (1800000 ÷ 100)
Average marks in mathematics of the class = 39%

Hence, the average marks in mathematics of the class is 39%. Therefore, the correct answer is Option B 39%.

Explanation:
The weighted average method is used to calculate the average of a set of values when each value has a different weight or importance. The weighted average formula is used to calculate the average of a set of values when each value has a different weight or importance. In the given problem, the total weight and total value of the class are calculated using the weighted average formula and then the average marks in mathematics of the class is calculated using the formula.

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Answer: Option C. -> Rs.5

Answer: Option C. -> Rs.21

The average wage per day paid by the contractor is Rs.21. To calculate the average wage, we need to find the total wages paid by the contractor.

Total wages paid by the contractor = Total amount paid to male workers + Total amount paid to female workers + Total amount paid to child workers

Total wages paid by the contractor = (20 x 25) + (15 x 20) + (5 x 8)
= 500 + 300 + 40
= Rs.840

Average wage per day = Total wages paid by the contractor / Total number of workers
= 840/40
= Rs.21

Hence, the average wage per day paid by the contractor is Rs.21.

Explanation of Average Wage:
Average wage is the sum of all wages paid by an employer divided by the total number of employees. It is the mean wage per employee per day or per week or per month. It is calculated by dividing the total wages paid by the employer by the total number of employees. It is used to measure the rate of wages paid by an employer.

Formula for Average Wage:
Average Wage = Total wages paid by the employer / Total number of employee
= W/N

Where,
W = Total wages paid by the employer
N = Total number of employee

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Answer: Option A. -> 2 years

Answer: Option C. -> 4 years

Answer: Option B. -> Rs. 5400
Let the original average expenditure per student be Rs. x. Then, the total expenditure of the hostel would be 100x.Given that to accommodate 20 more students, the average expenditure per student decreases by Rs. 5. Let the new average expenditure per student be Rs. (x - 5). Then, the new total expenditure of the hostel would be (100 + 20)(x - 5) = 120(x - 5) = 120x - 600.Also, given that the total expenditure increased by Rs. 400. Therefore, we have the equation:120x - 100x = 400 + 600=> 20x = 1000=> x = 50So, the original average expenditure per student was Rs. 50.The new average expenditure per student is Rs. (50 - 5) = Rs. 45.Therefore, the new total expenditure of the hostel is (100 + 20) * 45 = Rs. 5400.Hence, the correct option is (B) Rs. 5400.
Important formulas:

• Average expenditure = Total expenditure / Number of students
• Increase in expenditure = New expenditure - Original expenditure

Definitions:

• Average expenditure: The total expenditure divided by the number of units.
• Total expenditure: The sum of all the expenditures made on a particular item or group of items.
• Increase in expenditure: The amount by which the new expenditure exceeds the original expenditure.

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Answer: Option D. -> 24 Km.per hr.

Average Speed is defined as the total distance covered by an object divided by the total time taken. It is represented by the formula: Average Speed = Total Distance / Total Time.

From the question, the man went uphill with a speed of 20 km.p.h. and came downhill with a speed of 30 km.p.h. Therefore, the total distance covered and the total time taken need to be calculated in order to determine the average speed for his journey.

Total Distance = Distance Travelled Uphill + Distance Travelled Downhill

Total Time = Time Taken Uphill + Time Taken Downhill

Since the speed for both uphill and downhill is given, the distance travelled and time taken in both directions can be calculated using the formula: Distance = Speed × Time.

Distance Travelled Uphill = 20 km/h × Time Taken Uphill

Distance Travelled Downhill = 30 km/h × Time Taken Downhill

Now, the total distance and total time can be calculated:

Total Distance = Distance Travelled Uphill + Distance Travelled Downhill

Total Time = Time Taken Uphill + Time Taken Downhill

Finally, the average speed can be calculated using the formula: Average Speed = Total Distance / Total Time

Average Speed = Total Distance / Total Time

Therefore, the average speed for his journey is 24 km/h.

Hence, the correct answer is Option D. 24 Km.per hr.

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Answer: Option C. -> 12 Km. per hr.

Answer: Option B. -> \(33\frac{1}{3}\)

Answer: Option C. -> 665