A & B jointly made a profit of Rs.1650 and they decided to share it such that 1/3 of A's profit is equal to 2/5 of B's profit. Then profit of B is

Options

A. ₹ 700
B. ₹ 750
C. ₹ 850
D. ₹ 800

Answer

To solve the problem step by step, let's denote A's profit as \( A \) and B's profit as \( B \).

### Step 1: Set up the equations
We know that the total profit made by A and B is Rs. 1650. Therefore, we can write the equation:
\[ A + B = 1650 \]

### Step 2: Establish the relationship between A's and B's profits
According to the problem, \( \frac{1}{3} \) of A's profit is equal to \( \frac{2}{5} \) of B's profit. This gives us the equation:
\[ \frac{1}{3}A = \frac{2}{5}B \]

### Step 3: Rearranging the equation
To eliminate the fractions, we can cross-multiply:
\[ 5A = 6B \]
From this, we can express A in terms of B:
\[ A = \frac{6}{5}B \]

### Step 4: Substitute A in the total profit equation
Now, we substitute \( A \) in the first equation:
\[ \frac{6}{5}B + B = 1650 \]

### Step 5: Combine like terms
To combine the terms on the left side, we need a common denominator:
\[ \frac{6B}{5} + \frac{5B}{5} = 1650 \]
This simplifies to:
\[ \frac{11B}{5} = 1650 \]

### Step 6: Solve for B
To isolate \( B \), we multiply both sides by 5:
\[ 11B = 1650 \times 5 \]
Calculating the right side:
\[ 11B = 8250 \]

Now, divide both sides by 11:
\[ B = \frac{8250}{11} \]
Calculating this gives:
\[ B = 750 \]

### Step 7: Conclusion
Thus, the profit of B is Rs. 750.

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