Divide Rs 7,500 among A, B and C such that A's share to B's share is in ratio 5 : 2 and B's share to C's share is in the ratio `7 : 13`. How much will B receive?

Options

A. Rs 1,400
B. Rs 3,500
C. Rs 2,600
D. Rs 7,000

Answer

To solve the problem of dividing Rs 7,500 among A, B, and C based on the given ratios, we can follow these steps:

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

### Step 2: Express the Ratios in Terms of a Common Variable
Let’s denote:
- A's share = 5x
- B's share = 2x (from the first ratio)
- Now, we need to express C's share in terms of B's share. Since B's share to C's share is 7 : 13, we can say:
- B's share = 7y
- C's share = 13y

### Step 3: Equate B's Shares
From the two expressions for B's share, we have:
- 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 into A's and C's Shares
Now, substitute x back into the expressions for A's and C's shares:
- A's share = 5x = 5 * (7/2)y = (35/2)y
- B's share = 7y
- C's share = 13y

### Step 6: Write the Total Share
Now, we can express the total share in terms of y:
- Total share = A's share + B's share + C's share
- Total share = (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
- Total share = (35/2)y + (14/2)y + (26/2)y = (75/2)y

### Step 7: Set the Total Share Equal to Rs 7,500
Now, we know the total share equals Rs 7,500:
- (75/2)y = 7500

### Step 8: Solve for y
To find y, multiply both sides by 2:
- 75y = 15000
- y = 15000 / 75
- y = 200

### Step 9: Calculate B's Share
Now that we have y, we can find B's share:
- B's share = 7y = 7 * 200 = Rs 1400

### Conclusion
Thus, B will receive Rs 1,400.