X and Y enter into a partnership with capital in the ratio 3 ∶ 5 After 5 months X adds 50% of his capital, while Y withdraws 60% of his capital. What is the share (in Rs. lakhs) of X in the annual profit of Rs. 6.84 lakhs?
3.72
Analyzing Partnership Capital Investments
This question requires calculating a partner's profit share based on initial capital investments and subsequent changes. We need to determine the effective investment made by each partner (X and Y) over the entire year by considering the changes in their capital amounts after a specific period.
Step 1: Defining Initial Capital and Time Periods
Assume the initial capital invested by X is $3k$ and by Y is $5k$, reflecting their initial ratio of 3:5.
The total duration is 1 year (12 months).
The capital changes occur after the first 5 months.
- Investment Period 1: First 5 months
- Investment Period 2: Remaining 7 months (12 - 5 = 7 months)
Step 2: Calculating Capital After Changes
For Partner X:
- Initial Capital = $3k$
- After 5 months, X adds 50% of his capital.
- Capital Increase for X = $50\% \times 3k = 0.5 \times 3k = 1.5k$
- X's New Capital (for the remaining 7 months) = $3k + 1.5k = 4.5k$
For Partner Y:
- Initial Capital = $5k$
- After 5 months, Y withdraws 60% of his capital.
- Capital Withdrawal for Y = $60\% \times 5k = 0.6 \times 5k = 3k$
- Y's New Capital (for the remaining 7 months) = $5k - 3k = 2k$
Step 3: Calculating Total Investment Value
The profit share is distributed based on the ratio of the total investment values, calculated as (Capital $\times$ Time Period in months).
X's Total Investment Value:
- Investment for first 5 months = $3k \times 5 = 15k$
- Investment for remaining 7 months = $4.5k \times 7 = 31.5k$
- Total Investment for X = $15k + 31.5k = 46.5k$
Y's Total Investment Value:
- Investment for first 5 months = $5k \times 5 = 25k$
- Investment for remaining 7 months = $2k \times 7 = 14k$
- Total Investment for Y = $25k + 14k = 39k$
Step 4: Determining the Profit Sharing Ratio
The ratio of their total investment values determines how the profit is shared.
Ratio X : Y = $46.5k : 39k$
To simplify the ratio, we can remove $k$ and the decimal:
- Ratio = $46.5 : 39$
- Multiply by 10: $465 : 390$
- Divide by 5: $93 : 78$
- Divide by 3: $31 : 26$
The profit sharing ratio is X:Y = 31:26.
Step 5: Calculating X's Share of the Profit
The total annual profit is Rs. 6.84 lakhs.
The sum of the ratio parts = $31 + 26 = 57$.
X's share of the profit is calculated using his portion of the ratio:
X's Profit Share = $ \frac{\text{X's Ratio}}{\text{Total Ratio}} \times \text{Total Profit} $
X's Profit Share = $ \frac{31}{57} \times 6.84 \text{ lakhs} $
First, calculate $ \frac{6.84}{57} $:
$ \frac{6.84}{57} = 0.12 $
Now, multiply this by X's ratio part:
X's Profit Share = $ 31 \times 0.12 \text{ lakhs} $
X's Profit Share = $ 3.72 \text{ lakhs} $
Conclusion
Based on the calculations of capital investments over the year and the resulting profit sharing ratio, X's share in the annual profit of Rs. 6.84 lakhs is Rs. 3.72 lakhs.
Similar Questions
A, B and C did certain investments and the ratio of their time periods is 3 : 2 : 7 respectively. Ratio of the profits of A, B and C is 4 : 3 : 14 respectively. What is the ratio of the investments of A, B and C ?
A, B and C invested ₹40,000, ₹48,000 and ₹80,000, respectively, for a business at the start of a year. After six months, for the remaining time of the year, A added ₹4,000, B added ₹4,000 while C withdrew ₹4,000 every month. If the total profit is ₹6,72,000, then what is C's share (in ₹)?
A, B and C started a business in partnership. Initially, A invested Rs. 29,000, while B and C invested Rs. 25,000 each. After 4 months, A withdrew Rs. 3,000. After 2 more months, C invested Rs. 12,000 more. Find the share of C( in Rs.) in the profit of Rs. 33,200 at the end of the year.
A, B and C started a business with their capitals in the ratio 2 : 3 : 5. A increased his capital by 50% after 4 months, B increased his capital by \(33\frac{1}{3}\%\) after 6 months and C withdrew 50% of his capital after 8 months, from the start of the business. If the total profit at the end of a year was Rs. 86,800, then the difference between the shares of A and C in the profit was:
A, B and C invested capital in the ratio 5 : 7 : 4, the timing of their investments being in the ratio x : y : z. If their profits are distributed in the ratio 45 : 42 : 28, then x : y : z = ?
Profit of Rs. 42,500 has to be divided between three partners A, B and C in the ratio 3 ∶ 5 ∶ 9. How much (in Rs) does A get?
Profit of Rs. 12,400 has to be divided between three partners A, B, and C in the ratio 5 : 7 : 8. How much does B get (in Rs.)?
A, B and C started a business with the investment of Rs. 100000, Rs. 140000 and Rs. 200000 respectively. After 3 months, C left the business. 7 months after C left the business, B also left the business. B and C took their investments with them. At the end of the year, C received his share of profit as Rs. 1155. What is the total share of profits of A and B ?
A sum of Rs. x is divided among A, B and C such that the ratio of the shares of A and B is 6 ∶ 7 and that of B and C is 3 ∶ 2. If the difference between the shares of A and C is Rs. 540, then the value of x is∶
A, B and C start a business. A invests \(33\frac{1}{3}\%\) of the total capital, B invests 25% of the remaining and C invests the rest. If the total profit at the end of a year is Rs. 1,62,000 then A’s share in profit is:
Important Questions from Partnership
Kiran, Vimal and Naveen started a business by investing Rs. 1,35,000, Rs. 1,50,000 and Rs. 1,65,000 respectively. Find the share of each (respectively), out of an annual profit of Rs. 60,000.
When the incoming partner cannot bring premium for goodwill, then the necessary adjustment for goodwill is done through which one of the following?
A, B, C invest Rs. 20000, Rs. 30000, Rs. 40000 in a business. After one year, A withdrew his money but B and C continued for one more year. If the net profit after 2 years be Rs. 32000, then A’s share in the profit is:
Manoj received Rs. 6000 as his share out of the total profit of Rs. 9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs. 20000 for 6 months, whereas Ramesh invested his amount for the whole year, what was the amount invested by Ramesh?
Three friends A, B, and C invested Rs. 20,000, Rs. 18,000, and Rs. 14,000, respectively in a business. If at the end of the year they got a profit of Rs. 7,800, then the profit share of B would be:
