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)

Upstream speed = 50/5 = 10 km/h. Downstream speed = 80/4 = 20 km/h. Boat speed in still water = (10 + 20)/2 = 15 km/h.

Average of first n natural numbers = (n+1)/2 = 10.5. Therefore, n+1 = 21, so n = 20. Wait, if n=20, average = 21/2 = 10.5. But option shows B=21. Recalculating: (n+1)/2 = 10.5 gives n = 20. Let me verify with n=21: (21+1)/2 = 11. For average 10.5: n=20.

We need to find the initial work rate, then recalculate the time for the remaining job at an increased rate.

Step 1: Find the initial work rate

The worker completes \(\frac{1}{4}\) of the job in 5 days.

Step 2: Calculate the new work rate (increased by 25%)

A 25% increase means the new rate is \(1.25\) times the original rate.

Step 3: Find remaining work

The worker has completed \(\frac{1}{4}\) of the job, so the remaining work is:

Step 4: Calculate days needed for remaining work

Using \(\text{Time} = \frac{\text{Work}}{\text{Rate}}\):

Answer: The remaining job will take 12 days at the increased work rate. (Option A)

To find the time taken when both pipes work together, use the concept of work rates: the combined rate equals the sum of individual rates.

Step 1: Find individual work rates

Pipe A fills the tank in 12 hours, so its rate is \(\frac{1}{12}\) tank per hour.

Pipe B fills the tank in 15 hours, so its rate is \(\frac{1}{15}\) tank per hour.

Step 2: Find combined work rate

When both pipes work together:

Find the LCM of 12 and 15, which is 60:

Step 3: Calculate time to fill one tank

If the combined rate is \(\frac{3}{20}\) tank per hour, then time to fill 1 tank is:

Step 4: Convert to hours and minutes

Answer: Both pipes together fill the tank in \(6\) hours and \(40\) minutes (Option B)