Rs 68000 is divided among A, B and C in the ratio of `1/2 : 1/4: 5/16`. The difference of the greatest and the smallest part is :

Options

A. Rs 6000
B. Rs 14440
C. Rs 9200
D. Rs 16000

Answer

To solve the problem of dividing Rs 68000 among A, B, and C in the ratio of \( \frac{1}{2} : \frac{1}{4} : \frac{5}{16} \), we can follow these steps:

### Step 1: Convert the Ratios to a Common Denominator
The first step is to express the ratios with a common denominator. The denominators in the ratios are 2, 4, and 16. The least common multiple (LCM) of these numbers is 16.

- Convert \( \frac{1}{2} \) to have a denominator of 16:
\[ \frac{1}{2} = \frac{8}{16} \]
- Convert \( \frac{1}{4} \) to have a denominator of 16:
\[ \frac{1}{4} = \frac{4}{16} \]
- \( \frac{5}{16} \) remains the same.

Thus, the ratios become:
\[ A : B : C = 8 : 4 : 5 \]

### Step 2: Calculate the Total Parts
Now, we need to calculate the total number of parts in the ratio:
\[ 8 + 4 + 5 = 17 \text{ parts} \]

### Step 3: Determine the Value of Each Part
Next, we find the value of each part by dividing the total amount (Rs 68000) by the total number of parts (17):
\[ \text{Value of 1 part} = \frac{68000}{17} = 4000 \]

### Step 4: Calculate Individual Shares
Now we can calculate the individual shares for A, B, and C:
- A's share:
\[ A = 8 \times 4000 = 32000 \]
- B's share:
\[ B = 4 \times 4000 = 16000 \]
- C's share:
\[ C = 5 \times 4000 = 20000 \]

### Step 5: Find the Greatest and Smallest Shares
From the calculated shares:
- Greatest share = A's share = 32000
- Smallest share = B's share = 16000

### Step 6: Calculate the Difference
Finally, we find the difference between the greatest and smallest shares:
\[ \text{Difference} = 32000 - 16000 = 16000 \]

### Final Answer
The difference of the greatest and the smallest part is Rs 16000.

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