A sum of ₹ x is divided among A, B and C such that the ratio of shares of A and B is 3 : 4 and that of B and C is 5: 6. If C receives ₹1440 more than what A receives, then the value of x is

Options

A. 9280
B. 9000
C. 9440
D. 9600

Answer

To solve the problem step by step, we will follow the given ratios and the information provided.

### Step 1: Understand the Ratios
We have two ratios:
1. The ratio of shares of A and B is 3:4.
2. The ratio of shares of B and C is 5:6.

### Step 2: Express A, B, and C in Terms of a Common Variable
Let the shares of A, B, and C be represented as:
- A = 3k (for some variable k)
- B = 4k (from the first ratio)

Now, we need to express C in terms of B. Since B and C are in the ratio 5:6, we can express C as:
- B = 5m (for some variable m)
- C = 6m

### Step 3: Find a Common Variable for B
From the two expressions for B, we set them equal:
4k = 5m

Now we can express k in terms of m:
k = (5/4)m

### Step 4: Substitute k in A and C
Now we substitute k back into the expressions for A and C:
- A = 3k = 3 * (5/4)m = (15/4)m
- C = 6m

### Step 5: Set Up the Equation Based on the Given Information
According to the problem, C receives ₹1440 more than A:
C = A + 1440

Substituting the expressions we found:
6m = (15/4)m + 1440

### Step 6: Solve for m
To eliminate the fraction, multiply the entire equation by 4:
4 * 6m = 4 * (15/4)m + 4 * 1440
24m = 15m + 5760

Now, simplify:
24m - 15m = 5760
9m = 5760

Now, divide by 9:
m = 5760 / 9
m = 640

### Step 7: Find A, B, and C
Now we can find A, B, and C using m:
- B = 5m = 5 * 640 = 3200
- C = 6m = 6 * 640 = 3840
- A = (15/4)m = (15/4) * 640 = 2400

### Step 8: Calculate the Total Sum x
Now, we can find the total sum x:
x = A + B + C
x = 2400 + 3200 + 3840
x = 9440

### Final Answer
The value of x is ₹9440.

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