A sum of Rs 370 is to be divided among A, B and CC such that `("A's share")/("B's share") = ("B's share")/("C's share") 3/4`. A's share (in rupees) is:

Options

A. 240
B. 120
C. 100
D. 90

Answer

To solve the problem step-by-step, we will follow the given ratios and the total amount to find A's share.

### Step 1: Understand the Ratios
We are given that:
\[ \frac{A's \, share}{B's \, share} = \frac{B's \, share}{C's \, share} = \frac{3}{4} \]
This means that the ratio of A to B is 3:4 and the ratio of B to C is also 3:4.

### Step 2: Set Up the Ratios
Let:
- A's share = 3x
- B's share = 4x
- C's share = \( \frac{4}{3} \times B's \, share = \frac{4}{3} \times 4x = \frac{16}{3}x \)

### Step 3: Find a Common Variable
Since B's share appears in both ratios, we can express all shares in terms of B:
- A = 3y
- B = 4y
- C = \( \frac{4}{3} \times 4y = \frac{16}{3}y \)

### Step 4: Find the Total Shares
Now, we can find the total shares:
\[ A + B + C = 3y + 4y + \frac{16}{3}y \]
To add these, we need a common denominator. The common denominator for 1 and 3 is 3:
\[ = \frac{9y}{3} + \frac{12y}{3} + \frac{16y}{3} = \frac{37y}{3} \]

### Step 5: Set Up the Equation
We know that the total amount is Rs 370:
\[ \frac{37y}{3} = 370 \]

### Step 6: Solve for y
Multiply both sides by 3:
\[ 37y = 1110 \]
Now, divide by 37:
\[ y = \frac{1110}{37} = 30 \]

### Step 7: Find A's Share
Now that we have y, we can find A's share:
\[ A's \, share = 3y = 3 \times 30 = 90 \]

### Final Answer
A's share is Rs 90.

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