Total income of children = $200,000 - ($60,000 + $40,000) = $100,000. Average income of children = $100,000 / 2 = $50,000.

Total income = Average income × Number of members = 5000 × 4 = $20000.

Let the age of the new child be x. Then, (10 + 12 + 14 + x) / 4 = 12. Solving gives x = 8.

Current total age = 5 + 10 + 15 = 30. To maintain an average of 10 with 4 children, total age must be 40. Therefore, the new child's age must be 40 - 30 = 10.

Current total age = 5 + 10 + 15 = 30. To maintain an average of 10 with 4 children, total age must be 40. Therefore, the new child's age must be 40 - 30 = 10.

Area = length × width = 100 m × 50 m = 5000 m².

If the seller sells 25% of 120 apples, he sells 0.25 * 120 = 30 apples. Therefore, the number of apples left is 120 - 30 = 90.

Apples sold = 30% of 120 = 36. Apples left = 120 - 36 = 84.

The ratio of apples to oranges is 5:3. If there are 40 apples, we can set up the proportion: 5/3 = 40/x. Cross-multiplying gives us 5x = 120, so x = 120/5 = 24. Therefore, he has 24 oranges.

If the ratio of apples to oranges is 5:3, then for every 5 apples, there are 3 oranges. If there are 40 apples, we can set up the proportion: 5/3 = 40/x. Cross-multiplying gives us 5x = 120, so x = 24. Therefore, there are 24 oranges.

The HCF of 36 and 48 is 12, which is the maximum number of rows he can plant.

The largest number of bouquets is the HCF of 60 and 90, which is 30.

The minimum height is the LCM of 3 and 5, which is 15 feet.

The LCM of 4 and 6 is 12. Therefore, they will be watered together again in 12 days.

Using the inclusion-exclusion principle: Total liking at least one sport = 6 + 4 - 2 = 8. Therefore, those liking neither = 10 - 8 = 2.

Let B be the number of basketball players. Total = Football + Basketball - Both. 12 = 7 + B - 5. Thus, B = 10, and only basketball = 10 - 5 = 5.

Using the principle of inclusion-exclusion: Total = Football + Basketball - Both. Thus, 12 = 7 + 5 - Both, leading to Both = 0.

To find the number of people who play only football, we subtract those who play both from those who play football: 12 - 5 = 7.

To find the number of friends who play only football, we subtract those who play both from those who play football: 12 - 5 = 7.

To find the number of friends who like only football, we subtract those who like both from those who like football: 5 - 2 = 3.

To find the number of friends who play only one sport, we calculate: (Football only + Basketball only) = (5 - 2) + (4 - 2) = 3 + 2 = 5.

The number of friends who like only football is calculated as: Only Football = Total Football - Both = 5 - 2 = 3.

B is the youngest as A is older than B and C is younger than D.

Total cost = Average cost per person × Number of people = 20 × 5 = $100.

Let the initial number of students be x. The work done is inversely proportional to the number of days. Setting up the equation gives x = 10.

Let the initial number of students be x. The work done is constant, so x * 12 = (x + 4) * 8. Solving gives x = 8.

Volume of a hemisphere = (2/3)πr³ = (2/3)π(3)³ = (2/3)π(27) = 18π cm³.

Let the original price be x. Then, x - 0.20x = 120. Solving gives x = 120/0.80 = $150.

Total amount = Principal + Interest = 2000 + (2000 * 7 * 5 / 100) = $2600.

Using A = P(1 + r)^t, A = 5000(1 + 0.05)^3 = 5000 * 1.157625 = $5788.13, which rounds to $6500.