A sum of Rs 13,725 is divided between A, B, C and D such that the ratio of the shares of A and B is 3:4, that of B and C is 8:5 and that of C and D is 7:10. What is the share of C?

Options

A. Rs 2,625
B. Rs 2,475
C. Rs 3,150
D. Rs 3,750

Answer

To solve the problem of dividing Rs 13,725 among A, B, C, and D based on the given ratios, we will follow these steps:

### Step 1: Establish the Ratios
We have the following ratios:
- A : B = 3 : 4
- B : C = 8 : 5
- C : D = 7 : 10

### Step 2: Find a Common Ratio
To combine these ratios, we need to express them in terms of a common variable. We will express all ratios in terms of B.

From A : B = 3 : 4, we can express A as:
- A = (3/4)B

From B : C = 8 : 5, we can express C as:
- C = (5/8)B

From C : D = 7 : 10, we can express D as:
- D = (10/7)C = (10/7)(5/8)B = (50/56)B = (25/28)B

Now we have:
- A = (3/4)B
- B = B
- C = (5/8)B
- D = (25/28)B

### Step 3: Express All Shares in Terms of B
Now, we can express the total shares in terms of B:
- Total = A + B + C + D
- Total = (3/4)B + B + (5/8)B + (25/28)B

### Step 4: Find a Common Denominator
To add these fractions, we need a common denominator. The least common multiple of 4, 1, 8, and 28 is 56.

Now we convert each term:
- A = (3/4)B = (42/56)B
- B = (1)B = (56/56)B
- C = (5/8)B = (35/56)B
- D = (25/28)B = (50/56)B

### Step 5: Add the Shares
Now we can add these fractions:
- Total = (42/56)B + (56/56)B + (35/56)B + (50/56)B
- Total = (42 + 56 + 35 + 50)/56 * B
- Total = (183/56)B

### Step 6: Set the Total Equal to Rs 13,725
Now we set this equal to the total amount:
- (183/56)B = 13,725

### Step 7: Solve for B
To find B, we multiply both sides by (56/183):
- B = 13,725 * (56/183)

Calculating this gives:
- B = 4,000

### Step 8: Find C's Share
Now we can find C's share:
- C = (5/8)B = (5/8) * 4,000 = 2,500

### Conclusion
The share of C is Rs 2,500.

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