Five boxes of bananas cost Rs. 30 in total. At the same rate, how many boxes of bananas can you buy for Rs. 9?

Introduction / Context:
This question is a simple unitary method or proportion problem. It tests your ability to work with direct proportion between cost and quantity, which is a basic but important skill in arithmetic and everyday calculations involving prices and rates.

Given Data / Assumptions:

• Cost of 5 boxes of bananas = Rs. 30.

• The cost per box is constant; there are no discounts or bulk offers.

• We want to find how many boxes can be bought for Rs. 9 at the same rate.

Concept / Approach:
Since cost is directly proportional to the number of boxes, we can first find the cost of one box by dividing the total cost by the number of boxes. Once we have the cost per box, we divide the given amount of money (Rs. 9) by the cost per box to determine how many boxes can be bought. This is the standard unitary method: find the value for one unit, then scale up or down as required.

Step-by-Step Solution:
Total cost of 5 boxes = Rs. 30. Cost per box = 30 / 5 = Rs. 6. Available money = Rs. 9. Number of boxes that can be bought = 9 / 6. 9 / 6 = 1.5 boxes.

Verification / Alternative check:
To verify, consider how much 1.5 boxes would cost at Rs. 6 per box. Cost = 1.5 * 6 = Rs. 9, which matches the available money exactly. This confirms that the calculation is consistent. Note that mathematically, fractional boxes are allowed in the calculation, even though in real life you might only be able to buy whole boxes.

Why Other Options Are Wrong:
If you buy 2 boxes, you would need 2 * 6 = Rs. 12, which exceeds Rs. 9. For 1.25 boxes, the cost would be 1.25 * 6 = Rs. 7.5, which is less than Rs. 9 and does not use the full amount. Similarly, 2.5 boxes would cost 2.5 * 6 = Rs. 15, which is too much. Only 1.5 boxes correspond exactly to Rs. 9 at this rate.

Common Pitfalls:
Students sometimes try to use ratio directly without computing the cost per box, which can lead to mistakes if done hurriedly. Another common error is to reverse the division and compute 6 / 9 instead of 9 / 6. To avoid confusion, always determine the cost for one unit first, then divide the available money by that unit cost.

Final Answer:
At the given rate, you can buy 1.5 boxes of bananas for Rs. 9.