Question: 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
(4/9) of the total profit, what is the
value of 𝑥 (in ₹)?
(A) 2500
(B) 3000
(C) 4687
(D) 8437
Solution:
Let's calculate the value of x using the given information.
P invested ₹5000 per month for 6 months of the year, so the total investment made by P is ₹5000/month * 6 months = ₹30,000.
Q invested ₹x per month for 8 months of the year, so the total investment made by Q is ₹x/month * 8 months = ₹8x.
According to the given information, Q receives (4/9) of the total profit. This implies that Q's share of the profit is (4/9) of the total investment.
To find the value of x, we can set up the following equation:
Q's share of profit / Total investment = (4/9)
(8x) / (₹30,000 + ₹8x) = (4/9)
Now we can solve this equation to find the value of x.
Multiplying both sides of the equation by 9:
9 * (8x) = 4 * (₹30,000 + ₹8x)
72x = 120,000 + 32x
Subtracting 32x from both sides:
40x = 120,000
Dividing both sides by 40:
x = 120,000 / 40
x = 3,000
Therefore, the value of x (in ₹) is 3,000.
The correct answer is (B) 3000.