Since the average of x and y is 40, their sum x + y = 80. Adding z (10) makes the total sum 80 + 10 = 90. The average of the three numbers is 90 / 3 = 30.

Initial total weight = 25 * 40 = 1000 kg. Total weight with teacher = 26 * 41.5 = 1079 kg. Teacher's weight = 1079 - 1000 = 79 kg.

Total sum = 9 * 50 = 450. Sum of first 5 = 5 * 54 = 270. Sum of last 3 = 3 * 52 = 156. The 6th number = 450 - (270 + 156) = 450 - 426 = 24.

Total score = 40 + 50 + 45 + 60 + 30 = 225. Number of matches = 5. Average = 225 / 5 = 45.

When the same value is added to every number in a dataset, the average increases by that exact value. New average = 20 + 5 = 25.

If we add two consecutive numbers to a series, the average shifts by exactly 1 unit (since it's an arithmetic progression with common difference 1, shifted by 2 terms means average shifts by 2/2 = 1).

Total sum = 5 * 50 = 250. Sum of 4 terms = 45 + 42 + 119 + 84 = 290. 5th term = 250 - 290 = -40.

The multiples are 5, 10, ..., 50. This is an AP. Average = (First term + Last term)/2 = (5 + 50)/2 = 55/2 = 27.5.

Total of 5A + 4M = 9 * 36 = 324. Total of 7A + 8M = 15 * 48 = 720. Add both: 12A + 12M = 1044. Multiply by 2: 24A + 24M = 2088. But wait, average is over items. 5A+4M cost = 324. 7A+8M cost = 720. 12A+12M = 1044. So 24A+24M = 2088. If question implies cost of exactly those items. Let's provide correct option 2088. (Option b is 2088). Wait, if 5+4=9 items average 36, sum is 324. 7+8=15 items avg 48, sum is 720. 12 apples + 12 mangoes = 1044. 24 of each would be 2088. But let's check my option choice. I will pick 'b' if I edit, but I assigned 'a' 1044. I will adjust explanation to match: 12 apples + 12 mangoes = 1044. Oh wait, 24A+24M is asked. That's 2088. Let me set correct_option to b.

Current total = 10 * 32 = 320. Target total for 11 matches = 11 * 35 = 385. Runs required = 385 - 320 = 65.