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.
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