1. If \(b ∝ a^3\) and \(a\) increases in the ratio \(2:3\), then determine the ratio in which \(b\) increases.

2. If \(b ∝ a^2\) and \(a\) increases in the ratio \(2:3\), then determine the ratio in which \(b\) increases.

3. If \(b ∝ a^3\) and \(a\) increases in the ratio \(2 : 3\), then find the ratio in which \(b\) increases.

4. If \(y \propto x^3\) and \(x\) increases in the ratio \(2:3\), then determine the ratio in which \(y\) increases.

5. If \(b ∝ a^3\) and the increase in \(a\) is in the ratio \(2 : 3\), then determine the ratio of increase in \(b\).

6. Three friends purchase a bus by investing ₹1,20,000, ₹1,50,000, and ₹1,10,000 respectively. The first friend works as the driver, while the other two work as conductors. They decide that \(\frac{2}{5}\) of the income will be distributed based on work in the ratio 3 : 2 : 2, and the remaining amount will be divided according to their capital investment. If the total income in a certain month is ₹29,260, determine how much each person will receive.

7. John invests 800 INR for 5 months, and Paul invests 500 INR for 6 months in a business. The ratio in which the profit will be distributed between them is? (Question)

(a) 3:2 (b) 5:6 (c) 4:3 (d) 8:5

8. If two individuals invest \(a\) currency units and \(b\) currency units in a business for \(x\) and \(y\) months respectively, then their profit ratio is -

(a) \(ay:bx\) (b) \(ab:xy\) (c) \(ax:by\) (d) none of the above

9. Three household kerosene oil drums contained 800 liters, 725 liters, and 575 liters of oil respectively. The oil from these three drums was poured into a rectangular container, which then had a liquid depth of 7 decimeters. If the ratio of the length to the breadth of the rectangular container is 4:3, calculate and write the length and breadth of the container. Also, if the depth of the container were 5 decimeters instead, determine whether it could hold 1620 liters of oil.

10. When a spherical gas balloon is inflated and its radius increases from 7 cm to 21 cm, determine the ratio of its surface areas before and after inflation.

11. Ashish invested ₹600 for 5 months and Tarun invested ₹500 for 9 months to start a business. The ratio in which the profit will be distributed between them is —

(a) 3:2 (b) 4:3 (c) 6:5 (d) 2:3