Question

A, B and C are partners in a business. A receives \(\frac{3}{5}\) of the total profit while B and C share the remainder equally. A's profit is increased by ₹1,500, when the rate of profit is increased from 10% to 12% in a year. Then, B's share in the total profit is:

• A. ₹2,500
• B. ₹3,000
• C. ₹1,500
• D. ₹1,000

Answer 1

The Correct Option is A

To solve the problem, let's analyze the given information:

A receives \(\frac{3}{5}\) of the total profit. Therefore, B and C together share \(\frac{2}{5}\) of the total profit equally. When the profit rate increases from 10% to 12%, A's profit increase by ₹1,500.

Let the total investment be ₹\(P\).

Original profit rate is \(10\%\), so the original profit is \(0.1P\).

After the increase to \(12\%\), the new profit is \(0.12P\).

The increase in profit for A is given as ₹1,500, so:

\(0.12P \times \frac{3}{5} - 0.1P \times \frac{3}{5} = 1,500\)

\(0.02P \times \frac{3}{5} = 1,500\)

\(0.02 \times 0.6P = 1,500\)

\(0.012P = 1,500\)

Solving for \(P\),

\(P = \frac{1,500}{0.012} = 125,000\)

Now, let's determine B's share:

Total profit with 10% rate is \(0.1 \times 125,000 = 12,500\).

B and C share \(\frac{2}{5}\) of the profit: \(\frac{2}{5} \times 12,500 = 5,000\).

Since B and C share equally, B's share is:

\(B = \frac{5,000}{2} = 2,500\)

Thus, B's share in the total profit is ₹2,500.