rupes 750 is 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. rupes 350
B. rupes 260
C. rupes 140
D. rupes 250

Answer

To find A's share from the total amount of Rs 750 divided among A, B, and C in the given ratios, we can follow these steps:

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

### Step 2: Express B in terms of A and C
From the first ratio (A : B = 5 : 2), we can express B in terms of A:
- Let A = 5x and B = 2x for some value x.

From the second ratio (B : C = 7 : 13), we can express C in terms of B:
- Let B = 7y and C = 13y for some value y.

### Step 3: Equate the values of B
Since B is represented in both ratios, 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 into A and C
Now, we can express A and C in terms of y:
- 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):
- Total = A + B + C = (35/2)y + 7y + 13y
- To add these, convert 7y and 13y to have a common denominator:
- 7y = (14/2)y
- 13y = (26/2)y
- Total = (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
A's share is Rs 350.

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