P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year.
If at the end of that investment year, Q receives \(\frac{4}{9}\) of the total profit, what is the value of x (in ₹)?
(A) 2500
(B) 3000
(C) 4687
(D) 8437
Answer (2)
To solve this problem, we need to figure out how much Q invested each month so that his share of the profit matches the condition given.
First, let's determine the total investment made by both P and Q.
Investment by P:
P invested ₹5000 per month for 6 months.
Total investment by P = ₹5000 × 6 = ₹30,000
Investment by Q:
Suppose Q invested ₹x per month for 8 months.
Total investment by Q = ₹x × 8 = 8x
Given that Q receives 9 4 of the total profit, this implies that Q’s share of the total investment should also be 9 4 of the total investment.
Now, let's set up the equation based on this information:
Q's share of total investment = 9 4 .
The relationship between the investments is given by: 30000 + 8 x 8 x = 9 4
Let's solve for x :
Multiply both sides of the equation by 30000 + 8 x to clear the fraction: 8 x = 9 4 ( 30000 + 8 x )
Multiply both sides by 9 to solve for x : 72 x = 4 ( 30000 + 8 x )
Distribute the 4 on the right side: 72 x = 120000 + 32 x
Subtract 32 x from both sides to get: 40 x = 120000
Divide by 40 to isolate x : x = 40 120000 = 3000
Therefore, the value of x is ₹3000.
The correct answer is (B) 3000 .
By calculating the total investments made by P and Q, and recognizing the profit-sharing ratio, we found that Q must invest ₹3000 per month. This was determined through a series of equations based on their respective investments and the share of total profit. Therefore, the answer is (B) 3000.
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