The ratio of A's share to that B is 3 : 4. B gets 2/5 of Cs share. If Rs 425 are divided among therm, then A will get

Options

A. Rs 100
B. Rs 250
C. Rs 75
D. Rs 125

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Ratios
The ratio of A's share to B's share is given as 3:4. This means:
- A's share = 3 parts
- B's share = 4 parts

### Step 2: Determine B's Share in Relation to C
B receives \( \frac{2}{5} \) of C's share. To express this in terms of a ratio, we can set:
- Let C's share be represented as 5 parts (since B gets \( \frac{2}{5} \) of C's share).
- Therefore, B's share can be expressed as 2 parts.

Now we can express the ratio of B to C:
- B : C = 2 : 5

### Step 3: Combine the Ratios
Now we have two ratios:
1. A : B = 3 : 4
2. B : C = 2 : 5

To combine these ratios, we need to express them with a common value for B. The value of B in both ratios should be the same.

From A : B = 3 : 4, we can express B as 4 parts. From B : C = 2 : 5, we can express B as 2 parts.

To make B equal in both ratios, we can multiply the first ratio by 2:
- A : B = 3 * 2 : 4 * 2 = 6 : 8

Now we have:
- A : B = 6 : 8
- B : C = 2 : 5 (which we can multiply by 4 to make B = 8)
- B : C = 8 : 20

Now we can combine these ratios:
- A : B : C = 6 : 8 : 20

### Step 4: Calculate the Total Parts
Now we can add the parts together:
- Total parts = A + B + C = 6 + 8 + 20 = 34 parts

### Step 5: Find the Value of Each Part
The total amount to be divided is Rs 425. To find the value of each part:
- Value of each part = Total amount / Total parts = 425 / 34

Calculating this gives us:
- Value of each part = Rs 12.50 (approximately)

### Step 6: Calculate A's Share
Now we can find A's share:
- A's share = 6 parts
- A's share = 6 * 12.50 = Rs 75

### Final Answer
Thus, A will get Rs 75.

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