The problem requires calculating the difference in profit between partners X and Y, considering their initial investment ratio, a change in X's capital, and the total annual profit.
Investment Ratio and Initial Capital
The initial investment ratio of the three friends X, Y, and Z is given as $6:3:5$.
We are given that Z's investment is ₹12,000. Since Z's share in the ratio is 5 parts, we can determine the value of one part:
- Value of 1 part: $1 \text{ part} = \frac{₹12,000}{5} = ₹2,400$
- X's initial investment (6 parts): $X_{\text{initial}} = 6 \times ₹2,400 = ₹14,400$
- Y's investment (3 parts): $Y_{\text{initial}} = 3 \times ₹2,400 = ₹7,200$
Profit Sharing Ratio Calculation
Profit is distributed based on the investment amount and the duration. The total profit is annual (12 months).
- X's Profit Share: X invested his full capital for the first 6 months and then withdrew half (invested $\frac{1}{2}$ of his capital for the remaining 6 months).
X's effective investment ratio for the year is calculated considering time: $(6 \text{ months} \times 6 \text{ parts}) + (6 \text{ months} \times \frac{6}{2} \text{ parts}) = (6 \times 6) + (6 \times 3) = 36 + 18 = 54 \text{ (capital-time units)}$ - Y's Profit Share: Y invested his capital for the entire 12 months.
Y's effective investment ratio for the year is: $12 \text{ months} \times 3 \text{ parts} = 36 \text{ (capital-time units)}$ - Z's Profit Share: Z invested his capital for the entire 12 months.
Z's effective investment ratio for the year is: $12 \text{ months} \times 5 \text{ parts} = 60 \text{ (capital-time units)}$
The ratio for profit sharing is $X:Y:Z = 54:36:60$.
To simplify this ratio, we divide each term by their greatest common divisor, which is 6:
$ \frac{54}{6} : \frac{36}{6} : \frac{60}{6} = 9:6:10 $The final profit sharing ratio is $9:6:10$.
Individual Profit Calculation
The total annual profit is ₹69,000.
The sum of the parts in the simplified profit sharing ratio is $9 + 6 + 10 = 25$.
- X's Profit: $ \text{X's Profit} = \left(\frac{9}{25}\right) \times ₹69,000 $ $ \text{X's Profit} = 9 \times ₹2,760 = ₹24,840 $
- Y's Profit: $ \text{Y's Profit} = \left(\frac{6}{25}\right) \times ₹69,000 $ $ \text{Y's Profit} = 6 \times ₹2,760 = ₹16,560 $
Final Profit Difference
The question asks for the difference between X's profit and Y's profit.
$ \text{Difference} = \text{X's Profit} - \text{Y's Profit} $ $ \text{Difference} = ₹24,840 - ₹16,560 = ₹8,280 $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:
