**Question: **P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ 𝑥 per

month for 8 months of the year in a partnership business. The profit is shared in

proportion to the total investment made in that year.

If at the end of that investment year, Q receives

(4/9) of the total profit, what is the

value of 𝑥 (in ₹)?

(A) 2500

(B) 3000

(C) 4687

(D) 8437

**Solution:**

Let's calculate the value of x using the given information.

P invested ₹5000 per month for 6 months of the year, so the total investment made by P is ₹5000/month * 6 months = ₹30,000.

Q invested ₹x per month for 8 months of the year, so the total investment made by Q is ₹x/month * 8 months = ₹8x.

According to the given information, Q receives (4/9) of the total profit. This implies that Q's share of the profit is (4/9) of the total investment.

To find the value of x, we can set up the following equation:

Q's share of profit / Total investment = (4/9)

(8x) / (₹30,000 + ₹8x) = (4/9)

Now we can solve this equation to find the value of x.

Multiplying both sides of the equation by 9:

9 * (8x) = 4 * (₹30,000 + ₹8x)

72x = 120,000 + 32x

Subtracting 32x from both sides:

40x = 120,000

Dividing both sides by 40:

x = 120,000 / 40

x = 3,000

Therefore, the value of x (in ₹) is 3,000.

The correct answer is (B) 3000.