Rs. 750 are divided among A, B and C in such a manner that A:B = 5: 2 and B:C = 7:13. What is A's share ?

Options

A. Rs. 350
B. Rs. 260
C. Rs. 140
D. Rs. 250

Answer

To solve the problem of dividing Rs. 750 among A, B, and C based on the given ratios, we can follow these steps:

### Step 1: Understand the Ratios
We are given two ratios:
1. A : B = 5 : 2
2. B : C = 7 : 13

### Step 2: Express the Ratios in Terms of a Common Variable
Let’s express A, B, and C in terms of a common variable.
- From the first ratio (A : B = 5 : 2), we can write:
- A = 5x
- B = 2x

- From the second ratio (B : C = 7 : 13), we can express B in terms of another variable. Let’s denote B as 7y:
- B = 7y
- C = 13y

### Step 3: Equate the Two Expressions for B
Since B is represented in two different ways (2x and 7y), we can set them equal to each other:
- 2x = 7y

### Step 4: Solve for x in Terms of y
From the equation 2x = 7y, we can express x in terms of y:
- x = (7/2)y

### Step 5: Substitute x Back to Find A and C
Now we can substitute x back into the expressions for A and C:
- A = 5x = 5 * (7/2)y = (35/2)y
- B = 7y
- C = 13y

### Step 6: Find the Total Amount in Terms of y
Now we can find the total amount A + B + C:
- A + B + C = (35/2)y + 7y + 13y
- To combine these, convert 7y and 13y to have a common denominator:
- 7y = (14/2)y
- 13y = (26/2)y
- Therefore:
- A + B + C = (35/2)y + (14/2)y + (26/2)y = (75/2)y

### Step 7: Set the Total Equal to Rs. 750
Now we set the total equal to Rs. 750:
- (75/2)y = 750

### Step 8: Solve for y
To find y, multiply both sides by 2:
- 75y = 1500
- y = 1500 / 75
- y = 20

### Step 9: Find A's Share
Now that we have y, we can find A's share:
- A = (35/2)y = (35/2) * 20 = 350

### Conclusion
Thus, A's share is Rs. 350.