Profit Ratio Calculation
The total profit is Rs. 33,000. E's share is Rs. 15,000. Therefore, D's share is:
D's Profit = Total Profit - E's Profit
D's Profit = Rs. 33,000 - Rs. 15,000 = Rs. 18,000
The ratio of their profits is D:E = 18,000 : 15,000. Simplifying this ratio by dividing both by 3,000 gives:
Profit Ratio (D:E) = 6 : 5
Investment Calculation
Let the initial investment made by both D and E be Rs. x.
The business duration is 1 year (12 months).
- E's Investment: E invested Rs. x for the entire 12 months. Total investment by E = $x \times 12 = 12x$ months.
- D's Investment: D invested Rs. x for the first 4 months. After 4 months, D added Rs. 10,000. So, for the remaining 8 months (12 - 4 = 8), D invested Rs. $(x + 10,000)$. Total investment by D = $(x \times 4) + ((x + 10,000) \times 8)$ = $4x + 8x + 80,000$ = $12x + 80,000$ months.
Equating Ratios and Finding Initial Investment
The ratio of total investments must be equal to the ratio of profits.
Investment Ratio (D:E) = Profit Ratio (D:E)
$\frac{12x + 80,000}{12x} = \frac{6}{5}$
Cross-multiply to solve for x:
$5 \times (12x + 80,000) = 6 \times 12x$
$60x + 400,000 = 72x$
Subtract $60x$ from both sides:
$400,000 = 72x - 60x$
$400,000 = 12x$
Divide by 12:
$x = \frac{400,000}{12}$
$x = \frac{100,000}{3}$
$x \approx 33,333.33$
The initial investment was approximately Rs. 33,333.33.
Similar Questions
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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?
Which one of the following rights is usually not available to a partner consequent to the dissolution of a firm?
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?
