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
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:
Adesh and Bhadresh are partners sharing profits and losses in the ratio of 3 ∶ 2. Chandresh is admitted for 20% of share in profits out of which half of the share was gifted by Adesh and remaining was acquired by Chandresh from Adesh and Bhadresh in equal proportion. What would be new profit-sharing ratio?
Mathur started a business by investing R6,76,000 as capital. After 4 months, Goyal joined the business by investing a capital of Rs. 5,07,000. A total of Rs. 2,60,000 including 25% of the total profit was given to Goyal for conducting business at the end of the year. How much profit Mathur will get?
Mannu and Bhanu are partners. Bhanu wants to admit his son Channu into business. Can Channu become the partner of the firm?
L, S and D are partners sharing profits in the ratio of \(\frac{2}{5},\frac{3}{7}\) and \(\frac{3}{10}\). If S retires from the firm, what will be the gain ratio of L
