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

Options

A. A) Rs. 159
B. B) Rs. 96
C. C) Rs. 147
D. D) Rs. 105

Answer

To solve the problem step by step, we need to find the total amount of money based on the shares received by K, L, and M.

### Step 1: Understand the distribution of shares
From the problem, we know that:
- For every 1 rupee K receives, L receives 45 paisa and M receives 30 paisa.
- This means K's share is 1 rupee (100 paisa), L's share is 45 paisa, and M's share is 30 paisa.

### Step 2: Convert shares into a common unit
To make calculations easier, we can express all shares in terms of paisa:
- K = 100 paisa
- L = 45 paisa
- M = 30 paisa

### Step 3: Calculate the total share in paisa
Now, we can find the total share:
Total share = K + L + M = 100 paisa + 45 paisa + 30 paisa = 175 paisa

### Step 4: Determine the ratio of shares
Now, we can express the shares of K, L, and M in terms of a ratio:
- K : L : M = 100 : 45 : 30
To simplify this ratio, we can divide each term by 5:
- K : L : M = 20 : 9 : 6

### Step 5: Relate L's share to the total amount
We are given that L's share is Rs. 27. Since Rs. 1 = 100 paisa, Rs. 27 = 2700 paisa.

### Step 6: Set up the equation
From the ratio, we know that L's share corresponds to 9 parts out of a total of (20 + 9 + 6) = 35 parts. Therefore, we can set up the equation:
\[ \text{L's share} = \frac{9}{35} \times \text{Total Amount} \]
Substituting L's share:
\[ 2700 = \frac{9}{35} \times \text{Total Amount} \]

### Step 7: Solve for the total amount
To find the total amount, we can rearrange the equation:
\[ \text{Total Amount} = 2700 \times \frac{35}{9} \]
Calculating this gives:
\[ \text{Total Amount} = 2700 \times \frac{35}{9} = 2700 \times 3.8889 \approx 10500 \text{ paisa} \]
Converting this back to rupees:
\[ \text{Total Amount} = \frac{10500}{100} = 105 \text{ rupees} \]

### Final Answer
The total amount is **Rs. 105**.

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