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)

For consecutive odd numbers, the average equals the middle (4th) number. So 4th number = 39. The 7 numbers are: 33, 35, 37, 39, 41, 43, 45. Largest = 45.

Distance in first 2 hours = 50 × 2 = 100 km (which is 25% of total). Total distance = 400 km. Total time at 60 km/h = 400/60 = 6.67 hours.

Interest on first = 5,000 × 8 × 2 / 100 = 800. Interest on second = 7,500 × 12 × 2 / 100 = 1,800. Total interest = 2,600. Average rate = (2,600 × 100) / (12,500 × 2) = 10.4%.

Increase in total age = 38 - 28 = 10. If average increases by 2, then group size = 10/2 = 5.

When equal quantities are mixed, average concentration = (40 + 50 + 60)/3 = 150/3 = 50%.

CP of 3 items at 20% profit: 3 × (200/1.2) = 500. CP of 2 items at 25% loss: 2 × (300/0.75) = 800. Total CP = 1300, Total SP = 1500. Profit% = (200/1300) × 100 = 15.38/3.58 ≈ 4.29%.