01. If m : n = 6 : 7 and n = 19.6, then what is the value of m? Ops: A. 12.9 B. 21.4 C. 16.8 D. 24.6 Q 02. The population of a town has increased from 12,000 to 16,000. Find the percentage increase. Ops: A. 50% B. 45.67& C. 40% D. 33.33% Q 03. Rachel bought a bag for $750 and sold it for a loss of $32. What is the selling price of the bag? Ops: A. $825 B. $782 C. $718 D. $850 Q 04. The ratio of water and oil in a mixture of 72 litres is 11 : 13 . How many litres of water must be added to the mixture to make the ratio 5 : 4? Ops: A. 15.75 litres B. 14.89 litres C. 19.56 litres D. 22.75 litres Q 05. Jacob spends 8% of his income on transport and 60% of the remaining amount on food. After these expenses, he managed to save $662.4. His income is: Ops: A. $1000 B. $900 C. $1100 D. $1800 Q 06. If the cost price of an item is $840, the mark up is 15% and the discount is 10%, then find the profit percent. Ops: A. 3.5% B. 4.8% C. 6.2% D. 7% Q 07. Incomes of Sophia and Alice are in the ratio of 7 : 9 and each of them saves $360. Find Sophia's income, if the ratio of their expenditures is 2 : 3? Ops: A. $840 B. $1420 C. $1360 D. $1080

Sure, here are the answers to your questions:

Q 01. The ratio m : n = 6 : 7 means m/n = 6/7. If n = 19.6, we can substitute this into the equation to find m. So, m = (6/7) * 19.6 = 16.8. Therefore, the answer is C. 16.8.

Q 02. The percentage increase in population is calculated as (final value - initial value) / initial value * 100%. So, the percentage increase is (16,000 - 12,000) / 12,000 * 100% = 33.33%. Therefore, the answer is D. 33.33%.

Q 03. If Rachel sold the bag for a loss of $32, this means the selling price is the original price minus the loss. So, the selling price is$750 - $32 =$718. Therefore, the answer is C. $718.

Q 04. The total ratio of water and oil is 11 + 13 = 24. If the total mixture is 72 litres, this means each ratio is equivalent to 72 / 24 = 3 litres. To make the ratio 5 : 4, we need to add water. The total ratio after adding water should be 5 + 4 = 9. So, the amount of water to be added is (5 * 3) - (11 * 3) = -18 litres. Since we can't add a negative amount of water, this question seems to have a mistake.

Q 05. If Jacob spends 8% of his income on transport and 60% of the remaining on food, this means he saves 100% - 8% - (60% of 92%) = 36.8% of his income. If he saves $662.4, this means his income is$662.4 / 0.368 = $1800. Therefore, the answer is D.$1800.

Q 06. The mark up is the increase in the cost price, so the selling price is $840 + 15$840 = $966. The discount is a decrease in the selling price, so the final price is$966 - 10% of $966 =$869.4. The profit is the final price minus the cost price, so the profit is $869.4 -$840 = $29.4. The profit percent is the profit divided by the cost price times 100$29.4 / $840 * 100% = 3.5%. Therefore, the answer is A. 3.5%.

Q 07. If the incomes of Sophia and Alice are in the ratio 7 : 9, and the ratio of their expenditures is 2 : 3, this means the ratio of their savings is also 7 : 9 (since income - expenditure = savings). If each of them saves $360, this means Sophia's income is 7 parts of the total savings, so Sophia's income is 7 *$360 = $2520. Therefore, none of the options match the correct answer.