P and Q start a business. P invests ₹90,000 for 8 months, Q invests ₹1,50,000 for 5 months. What is Q's share of a ₹50,000 profit(approximate)?

The correct answer is ₹25,510.

Step-by-Step Explanation:

In a business partnership, the profit is divided among the partners in the ratio of the product of their invested capital and the time period for which it is invested.

1. Calculate the Investment-Time Product for P and Q:
For P:
Capital invested = ₹90,000
Time duration = 8 months
$\text{Product for P}=90000\times 8=\mathrm{7,20,000}$

For Q:
Capital invested = ₹1,50,000
Time duration = 5 months
$\text{Product for Q}=150000\times 5=\mathrm{7,50,000}$

2. Determine the Ratio of Profit Sharing:
Ratio of P's share to Q's share = 7,20,000 : 7,50,000
Dividing both sides by 30,000:
$\text{Ratio (P : Q)}=24:25$

3. Calculate Q's Share of the Profit:
Total ratio parts = 24 + 25 = 49 parts
Total profit = ₹50,000

Q's share is calculated as:
$\text{Q's Share}=\left(\frac{25}{49}\right)\times 50000$

$\text{Q's Share}=\frac{1250000}{49}\approx 25510.20$

Approximating to the nearest whole rupee, Q's share of the profit is ₹25,510.