Rs.680 has been divided among A,B,C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets then B'S share is

Options

A. Rs.60
B. Rs.80
C. Rs.120
D. Rs.160

Answer

To solve the problem step by step, we will first establish the relationships between A, B, and C based on the information given.

### Step 1: Establish the relationships
According to the problem:
- A gets \( \frac{2}{3} \) of what B gets.
- B gets \( \frac{1}{4} \) of what C gets.

Let’s denote:
- B's share as \( B \).
- A's share as \( A = \frac{2}{3}B \).
- C's share as \( C = 4B \) (since B gets \( \frac{1}{4} \) of C, we can express C in terms of B).

### Step 2: Write the total amount
The total amount distributed among A, B, and C is Rs. 680. Therefore, we can write the equation:
\[ A + B + C = 680 \]
Substituting the expressions for A and C in terms of B:
\[ \frac{2}{3}B + B + 4B = 680 \]

### Step 3: Combine like terms
To combine the terms, first convert \( B \) and \( 4B \) into a common fraction:
\[ \frac{2}{3}B + \frac{3}{3}B + \frac{12}{3}B = 680 \]
This simplifies to:
\[ \frac{2 + 3 + 12}{3}B = 680 \]
\[ \frac{17}{3}B = 680 \]

### Step 4: Solve for B
Now, we can solve for B by multiplying both sides by \( \frac{3}{17} \):
\[ B = 680 \times \frac{3}{17} \]
Calculating the right side:
\[ B = 680 \div 17 \times 3 \]
Calculating \( 680 \div 17 \):
\[ 680 \div 17 = 40 \]
So,
\[ B = 40 \times 3 = 120 \]

### Conclusion
Thus, B's share is Rs. 120.