Investment Ratio Setup
Let the initial investments of partners P, Q, and R be $6x$, $7x$, and $9x$ respectively, according to the initial ratio $6 : 7 : 9$.
Investment Additions
After one year, additional amounts are added to their investments:
- P adds ₹30,000. P's new investment = $6x + 30000$.
- Q adds ₹25,000. Q's new investment = $7x + 25000$.
- R adds an unknown amount, let's denote it as $A$. R's new investment = $9x + A$.
New Investment Ratio
The investments are now in a new ratio of $8 : 9 : 11$.
Solving for Investment Factor
We can establish a proportion using the new investments of P and Q:
$ \frac{6x + 30000}{7x + 25000} = \frac{8}{9} $Cross-multiplying to solve for $x$:
$ 9(6x + 30000) = 8(7x + 25000) $ $ 54x + 270000 = 56x + 200000 $Rearranging the terms to isolate $x$:
$ 56x - 54x = 270000 - 200000 $ $ 2x = 70000 $ $ x = \frac{70000}{2} $ $ x = 35000 $Calculating Partner R's Added Amount
First, calculate Q's new investment using the value of $x$:
$ \text{Q's new investment} = 7x + 25000 = 7(35000) + 25000 = 245000 + 25000 = 270000 $Now, use the ratio between Q's and R's new investments to find $A$. The new ratio for Q : R is $9 : 11$.
$ \frac{\text{Q's new investment}}{\text{R's new investment}} = \frac{9}{11} $ $ \frac{270000}{9x + A} = \frac{9}{11} $We know $9x = 9(35000) = 315000$. Substitute this value:
$ \frac{270000}{315000 + A} = \frac{9}{11} $Cross-multiply:
$ 11 \times 270000 = 9(315000 + A) $ $ 2970000 = 2835000 + 9A $Solve for $9A$:
$ 9A = 2970000 - 2835000 $ $ 9A = 135000 $Finally, solve for $A$:
$ A = \frac{135000}{9} $ $ A = 15000 $Thus, the amount added by partner R is ₹15,000.
Similar Questions
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Important Questions from Partnership
Three partners X, Y and Z started their business by investing ₹40,000, ₹38,000 and ₹30,000, respectively. After 6 months, X and Z made additional investments of ₹20,000 and ₹15,000 respectively, whereas Y withdrew ₹8,000. Find the share of Y (in ₹) in the total profit of ₹38,880 made at the end of the year.
A, B and C invested their capitals in the ratio 2 ∶ 3 ∶ 5. The ratio of months for which they invested is 4 ∶ 2 ∶ 3, respectively. If the difference between the profit shares of A and B is Rs. 1,86,000, then C's share of profit (in Rs.) is:
A started a business with a capital of Rs. 54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided among the three in the ratio 1 ∶ 4 ∶ 5. What is the sum (in Rs.) of the capitals invested by B and C?
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 invest in a business in the ratio 4 ∶ 5 ∶ 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make Rs 36,000 profit of which 25% is reinvested in the business, how much does B get (in Rs)?
