Sum of 5 friends = 5 × 24 = 120. Sum of 4 friends = 4 × 22 = 88. Age of friend who left = 120 - 88 = 32 years.

Total cost = (10 × 50) + (15 × 40) = 500 + 600 = 1100. Total items = 25. Average = 1100/25 = ₹44.

Sum of 6 numbers = 6 × 18 = 108. Sum of 3 numbers = 3 × 24 = 72. Total sum = 180. Total numbers = 9. New average = 180/9 = 20.

Total distance = 120 + 180 = 300 km. Total time = 2 + 3 = 5 hours. Average speed = 300/5 = 60 km/h.

Sum needed for average 85 in 4 subjects = 4 × 85 = 340. Sum of 3 scores = 75 + 82 + 88 = 245. Fourth subject score = 340 - 245 = 95.

To find C's weight, use the definition of average: the sum of all values divided by the count equals the average.

Step 1: Set up the average formula

The average weight of A, B, and C is 70 kg, so:

Step 2: Express the sum of weights

Multiply both sides by 3 to find the total weight:

Step 3: Substitute known values

We know A = 75 kg and B = 68 kg. Substitute into the equation:

Step 4: Solve for C's weight

Answer: C's weight is \(67\,\text{kg}\) (Option C)

To find the new average, we must first calculate the total score change when a student leaves and a new student joins.

Step 1: Find the Total Score of Original 5 Students

The average of 5 students is 78, so we multiply the average by the number of students to get the total.

Step 2: Calculate the New Total Score

When a student scoring 68 leaves, we subtract 68. When a new student scoring 88 joins, we add 88.

Step 3: Find the New Average

The number of students remains 5. Divide the new total by 5 to get the new average.

The new average is 82.

Answer: (B) 82

Sum of 4 numbers = 35 × 4 = 140. Sum of 3 numbers = 28 + 36 + 42 = 106. Fourth number = 140 - 106 = 34.

Average speed is the total distance traveled divided by the total time taken, calculated as \(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\).

Step 1: Calculate total distance

The train travels in two segments:

Step 2: Calculate total time

The train travels for two different periods:

Step 3: Apply the average speed formula

Step 4: Simplify the division

Total distance traveled:

200+150=350 km

Total time taken:

4+2.5=6.5 hours

Average speed:

Average Speed=

Total Time

Total Distance

​

=

6.5

350

​

=

13

700

​

≈53.85 km/h

Therefore, the average speed is approximately 53.85 km/h.

Answer: The average speed is approximately \(53.85 \text{ km/h}\) (Option C)

Rate of worker 1 = 1/8, worker 2 = 1/12. Combined rate = 1/8 + 1/12 = (3+2)/24 = 5/24. Time = 24/5 = 4.8 days.