On her deathbed, a grand mother called upon his three grand sons and told them to distribute all her assets worth Rs. 52,500 in the ratio of 1/35 : 1/21 : 1/15 amongst themselves. Find the smallest share amongst the three portions ?

Options

A. A) Rs. 5422
B. B) Rs. 10,500
C. C) Rs. 12,800
D. D) Rs. 15,000

Answer

To solve the problem of distributing the assets worth Rs. 52,500 among the three grandsons in the given ratio, we will follow these steps:

### Step 1: Determine the Ratios
The given ratios are:
- Grandson 1: \( \frac{1}{35} \)
- Grandson 2: \( \frac{1}{21} \)
- Grandson 3: \( \frac{1}{15} \)

### Step 2: Find a Common Denominator
To compare these fractions, we need to find a common denominator. The denominators are 35, 21, and 15.

The least common multiple (LCM) of these numbers is 105.

### Step 3: Convert the Ratios
Now, we convert each ratio to have the common denominator of 105:
- Grandson 1: \( \frac{1}{35} = \frac{3}{105} \)
- Grandson 2: \( \frac{1}{21} = \frac{5}{105} \)
- Grandson 3: \( \frac{1}{15} = \frac{7}{105} \)

### Step 4: Write the Ratios in Whole Numbers
Now we can express the ratios in whole numbers:
- Grandson 1: 3
- Grandson 2: 5
- Grandson 3: 7

### Step 5: Calculate the Total Parts
Add the parts together:
\[ 3 + 5 + 7 = 15 \]

### Step 6: Calculate the Value of Each Part
Now, we can find the value of each part by dividing the total assets by the total parts:
\[ \text{Value of each part} = \frac{52,500}{15} = 3,500 \]

### Step 7: Calculate Each Grandson's Share
Now we can calculate each grandson's share:
- Grandson 1's share: \( 3 \times 3,500 = 10,500 \)
- Grandson 2's share: \( 5 \times 3,500 = 17,500 \)
- Grandson 3's share: \( 7 \times 3,500 = 24,500 \)

### Step 8: Identify the Smallest Share
From the shares calculated:
- Grandson 1: Rs. 10,500
- Grandson 2: Rs. 17,500
- Grandson 3: Rs. 24,500

The smallest share is Rs. 10,500.

### Final Answer
The smallest share amongst the three portions is **Rs. 10,500**.

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