Rajesh started a business by investing ₹1,00,000. After 5 months, Suresh joined with ₹1,50,000. At the end of 7 months from the start, Tushar joined with ₹2,00,000. If the total profit is ₹1,50,000 at the end of the year, find the share of Tushar(approximate) .

`. Let's construct the response directly. ₹46,154

Correct Option: ₹46,154

Step-by-Step Explanation:

In a partnership business, the profit earned at the end of a period is distributed among the partners in the ratio of the product of their investments and the respective time periods for which the investments were made.

1. Determine the time period for each partner:
The business runs for a total of 1 year (12 months).

• Rajesh: Invested ₹1,00,000 right from the start for the entire 12 months.
• Suresh: Joined 5 months after the start, so his investment was active for:

$12-5=7\text{months}$

• Tushar: Joined at the end of 7 months from the start, so his investment was active for:

$12-7=5\text{months}$

2. Calculate the equivalent investment-time product for each partner:

• Rajesh's product:

$\text{₹}\mathrm{1,00,000}\times 12=\mathrm{12,00,000}$

• Suresh's product:

$\text{₹}\mathrm{1,50,000}\times 7=\mathrm{10,50,000}$

• Tushar's product:

$\text{₹}\mathrm{2,00,000}\times 5=\mathrm{10,00,000}$

3. Find the ratio of their profit shares:

$\text{Rajesh}:\text{Suresh}:\text{Tushar}=\mathrm{12,00,000}:\mathrm{10,50,000}:\mathrm{10,00,000}$

Simplifying the ratio by dividing each term by 50,000:

$\text{Rajesh}:\text{Suresh}:\text{Tushar}=24:21:20$

4. Calculate Tushar's share of the profit:

Sum of the ratio terms:

$24+21+20=65$

Total profit = ₹1,50,000.
Tushar's share is given by:

$\text{Tushar's Share}=\left(\frac{20}{65}\right)\times \mathrm{1,50,000}$

Simplifying the fraction:

$\text{Tushar's Share}=\left(\frac{4}{13}\right)\times \mathrm{1,50,000}$

$\text{Tushar's Share}=\frac{\mathrm{6,00,000}}{13}\approx \text{₹}\mathrm{46,153.85}$

Approximating to the nearest rupee, Tushar's share is ₹46,154.