Discount = 150 - 120 = 30. Discount percentage = (30 / 150) * 100 = 20%.

30% of $80 = $24. Final price = $80 - $24 = $56.

Distance = height / tan(60) = 100 / √3 = 100/√3 = 50 meters

Length of string = height / sin(30) = 40 / 0.5 = 80 meters.

Distance = height / tan(angle) = 60 / (√3) = 20√3 meters.

Work done by first man in one day = 1/10. Work done by second man in one day = 1/15. Together they do = 1/10 + 1/15 = 1/6. Therefore, they will complete the work in 6 days.

Work done in 1 day = 1/10. Work done in 3 days = 3 × (1/10) = 3/10.

Time = Distance / Speed = 20 km / 5 km/h = 4 hours.

Let the original salary be x. After a 20% raise, x + 0.2x = 1.2x = 1200. Thus, x = 1200 / 1.2 = 1000.

Let the original salary be x. After a 20% raise, the salary is x + 0.2x = 1.2x. Given 1.2x = 1200, we find x = 1200 / 1.2 = 1000.

Daily earnings = $500 / 5 days = $100. Earnings in 15 days = $100 * 15 = $1500.

Distance = Speed × Time = 4 km/h × 2.5 h = 10 km.

Water = 70% of 100 liters = 0.7 * 100 = 70 liters.

Sugar in the mixture = 25% of 40 liters = 0.25 * 40 = 10 liters.

Total mixture = 5 + 10 = 15 liters. Percentage of A = (5/15) * 100 = 33.33%.

10% of 90 liters = (10/100) * 90 = 9 liters of oil.

Total parts = 3 + 2 = 5. Percentage of A = (3/5) * 100 = 60%.

30 days = 4 weeks + 2 days. If the month starts on a Friday, the last day will be 2 days later, which is a Saturday.

30 days = 4 weeks + 2 days, which is approximately 4.29 weeks, but the closest whole number is 4 weeks.

Let the daughter's age be x. Then the mother's age is 6x. In 6 years, the mother will be 6x + 6 and the daughter will be x + 6. The equation is 6x + 6 = 4(x + 6), which simplifies to 6x + 6 = 4x + 24, so 2x = 18, and x = 9.

A number that gives a remainder of 4 when divided by 6 can be expressed as 6k + 4. For k = 2, the number is 6*2 + 4 = 16.

Let the number be x. The equation is 3x - 9 = 0. Solving gives x = 3.

Let the number be x. The equation is 9x - 9 = 72. Adding 9 to both sides gives 9x = 81, so x = 81/9 = 9.

Loss = Cost Price - Selling Price = 80 - 64 = 16. Loss Percentage = (Loss/Cost Price) * 100 = (16/80) * 100 = 20%.

Work done in 1 day = 1/10. Work done in 3 days = 3 * (1/10) = 3/10.

Rate = (Simple Interest × 100) / (Principal × Time) = (120 × 100) / (800 × 2) = 7.5%.

Let the original salary be x. After a 20% raise, the salary is x + 0.2x = 1.2x. Therefore, 1.2x = 1200, so x = 1200 / 1.2 = $1000.

Rate = (Interest * 100) / (Principal * Time) = (180 * 100) / (1200 * 3) = 5%.

Spending = 60% of 5000 = 3000. Savings = 5000 - 3000 = $2000.

Selling Price = Cost Price + Profit = 50 + (20% of 50) = 50 + 10 = $60