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 \( \frac{4}{9} \) of the total profit, what is the value of \( x \) (in ₹)?

• A. 2500
• B. 3000
• C. 4687
• D. 8437

Hint:

To find the amount invested by each partner, use the ratio of their investments to the total investment. The share of profit is then directly proportional to this ratio.

Answer 1

The Correct Option is B

Let's calculate the total investment made by P and Q. P invests ₹5000 per month for 6 months, so P's total investment is: \[ 5000 \times 6 = 30,000 \, \text{₹}. \] Q invests ₹x per month for 8 months, so Q's total investment is: \[ x \times 8 = 8x \, \text{₹}. \] The total investment made by both P and Q is: \[ 30,000 + 8x \, \text{₹}. \] The total profit is shared in proportion to the total investment. We are given that Q receives \( \frac{4}{9} \) of the total profit. Therefore, the fraction of the total profit received by Q is the ratio of Q's investment to the total investment, i.e., \[ \frac{8x}{30,000 + 8x}. \] Since Q receives \( \frac{4}{9} \) of the total profit, we can set up the equation: \[ \frac{8x}{30,000 + 8x} = \frac{4}{9}. \] Cross-multiply to solve for \( x \): \[ 9 \times 8x = 4 \times (30,000 + 8x), \] \[ 72x = 120,000 + 32x, \] \[ 72x - 32x = 120,000, \] \[ 40x = 120,000, \] \[ x = \frac{120,000}{40} = 3000. \] Thus, the value of \( x \) is ₹3000.