Q1. A cyclist covers a distance of 45 km in 1.5 hours. What is his average speed?
Solution:
Average speed = total distance / total time. Thus, average speed = 45 km / 1.5 h = 30 km/h.
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Q2. In a certain mixture, the ratio of sugar to water is 1:4. If 2 liters of sugar is added to the mixture, what will be the new ratio of sugar to water if the initial amount of water was 8 liters?
Solution:
Initial sugar = 1 part, water = 4 parts (8 liters). After adding 2 liters of sugar, new sugar = 2 liters, water = 8 liters. Ratio = 2:8 = 1:4.
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Q3. A store sells a laptop for $800 after applying a discount of 20%. What was the marked price?
Solution:
Let the marked price be x. After a 20% discount, the selling price is 0.80x = $800. Therefore, x = $800 / 0.80 = $1000.
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Q4. If a shopkeeper sells an item for $80 after a discount of 20%, what was the marked price?
Solution:
Let the marked price be x. After a 20% discount, the selling price is x - (0.20 * x) = 0.80x. Setting this equal to $80 gives 0.80x = $80, so x = $80 / 0.80 = $100.
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Q5. If a product is bought for $150 and sold for $120, what is the percentage loss incurred?
Q6. A recipe requires sugar and flour in the ratio of 1:4. If you have 200 grams of flour, how much sugar do you need?
Solution:
The ratio of sugar to flour is 1:4. If you have 200 grams of flour, then the amount of sugar needed is (1/4) * 200 = 50 grams.
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Q7. A sum of money is invested at a certain rate of compound interest. If the amount becomes three times in 10 years, what is the annual interest rate?
Solution:
Using the formula A = P(1 + r)^n, we have 3P = P(1 + r)^10. Thus, (1 + r)^10 = 3. Solving gives r ≈ 0.15 or 15%.
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Q8. A man spends 30% of his salary on rent and 20% on groceries. If his salary is $1000, how much does he spend on groceries?
Solution:
If the man's salary is $1000, he spends 20% on groceries. Therefore, the amount spent on groceries is 0.2 * 1000 = $200.
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Q9. If the average of five numbers is 30, what is the sum of those numbers? (2023)
Solution:
Sum of the numbers = Average × Number of items = 30 × 5 = 150.
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Q10. 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 20 liters?
Solution:
Initially, there is 1 part sugar and 4 parts water, totaling 5 parts. In 20 liters, there are 4 liters of sugar and 16 liters of water. After adding 2 liters of sugar, the new ratio is 6:16, which simplifies to 1:5.
