A sum of money is divided among K, L and M in such a way that for each rupee K receives, L receives 45 paise and M receives 30 paise. If the share of L is Rs 27, what is the total amount of money?

Introduction / Context:
This question is about sharing a sum of money among three people according to a ratio expressed in rupees and paise. The distribution rule is that for every rupee K receives, L and M receive specified amounts in paise. We are also told the actual share of L and must deduce the total amount distributed. It is a practical ratio and proportion problem with unit conversion between rupees and paise.

Given Data / Assumptions:

• For each rupee K gets, L gets 45 paise and M gets 30 paise.
• 1 rupee = 100 paise.
• L's actual share is Rs 27.
• We need to find the total of all three shares together.

Concept / Approach:
We first convert all amounts to a common unit, typically paise, to avoid confusion. If we treat K's unit share as 100 paise, then L's share is 45 paise and M's share is 30 paise for the same underlying unit. This gives a ratio between K, L and M. Once we express L's actual amount in terms of this ratio, we can find the scaling factor and therefore compute the total amount corresponding to the entire ratio.

Step-by-Step Solution:
For each rupee K gets, K's share in paise is 100. L's share for the same unit is 45 paise. M's share for the same unit is 30 paise. Thus K : L : M = 100 : 45 : 30. Divide by 5 to simplify: 20 : 9 : 6. So the ratio is K : L : M = 20 : 9 : 6. L's share corresponds to 9 parts. We are told L receives Rs 27. One part is therefore 27 / 9 = Rs 3. Total parts = 20 + 9 + 6 = 35. Total amount = 35 * 3 = Rs 105.

Verification / Alternative check:
We can compute each person's share explicitly. K gets 20 * 3 = Rs 60. L gets 9 * 3 = Rs 27, which matches the question. M gets 6 * 3 = Rs 18. Adding them gives 60 + 27 + 18 = Rs 105. This confirms that the total amount calculated is consistent with both the ratio and L's individual share.

Why Other Options Are Wrong:
Totals such as Rs 96, Rs 147 or Rs 159 do not yield L's share as exactly Rs 27 when the ratio 20 : 9 : 6 is applied. Rs 135 is another distracting value that does not produce integer shares respecting the given distribution rule. Only Rs 105 aligns with all the data and the established ratio.

Common Pitfalls:
One common mistake is to use the numbers 1, 0.45 and 0.30 directly as the ratio without converting to a uniform unit such as paise, which can lead to confusion. Another is to forget to simplify the ratio before scaling up. Working in paise and then converting back to rupees at the end helps maintain clarity.

Final Answer:
The total amount of money divided among K, L and M is Rs 105.