Q1. A person invests $2000 at a rate of 6% per annum. How much interest will he earn in 4 years under simple interest? (2023)
Solution:
Using SI = P * r * t / 100, we have SI = 2000 * 6 * 4 / 100 = $480.
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Q2. A person invests $2000 at a compound interest rate of 8% per annum. What will be the total amount after 2 years? (2000)
Solution:
Using the formula A = P(1 + r)^t, A = 2000(1 + 0.08)^2 = 2000 * 1.1664 = $2332.80, which rounds to $2320.
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Q3. In a mixture of two liquids, if the first liquid is 40% and the second is 60%, what is the overall percentage of the first liquid in a 50-liter mixture containing 20 liters of the first liquid?
Solution:
Percentage of first liquid = (20/50) * 100 = 40%.
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Q4. A discount of 15% on a product results in a selling price of $255. What was the marked price?
Solution:
Let the marked price be x. Selling Price = x - (0.15 * x) = 0.85x. Setting this equal to $255 gives 0.85x = $255, so x = $255 / 0.85 = $300.
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Q5. In a race, the average speed of a runner is 10 km/h. If he runs for 2 hours and then walks for 1 hour at 5 km/h, what is his average speed for the entire journey?
Solution:
Distance covered while running = 10 km/h × 2 h = 20 km. Distance covered while walking = 5 km/h × 1 h = 5 km. Total distance = 25 km, total time = 3 h. Average speed = 25 km / 3 h = 8.33 km/h.
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Q6. In a certain mixture, the ratio of sugar to water is 1:4. If 2 liters of sugar is added, what will be the new ratio if the total volume of the mixture is 10 liters?
Solution:
Initial sugar = 1 part, water = 4 parts. Total = 5 parts. New sugar = 2 liters, water = 8 liters. Ratio = 2:8 = 1:4.
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Q7. If the difference between the compound interest and simple interest on a certain sum of money for 2 years at 10% is $50, what is the principal? (2000)
Solution:
The difference between CI and SI for 2 years is given by P * (r^2)/100^2. Setting this equal to $50 and solving gives P = $1500.
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Q8. In how many years will a sum of money triple itself at 10% per annum compound interest? (2023)
Solution:
Using the formula A = P(1 + r)^n, we set 3P = P(1 + 0.1)^n. Solving gives n ≈ 12 years.
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Q9. A student scored 90 marks out of 120 in a test. What is the percentage score of the student? (2023)
Solution:
Percentage score = (90 / 120) * 100 = 75%.
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Q10. A mixture contains milk and water in the ratio of 3:2. If the total volume of the mixture is 50 liters, how much milk is there?
Solution:
In the ratio of 3:2, the total parts = 3 + 2 = 5. The amount of milk is (3/5) * 50 liters = 30 liters.
