Discussion
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 ₹)?
Answer: B
The value of \(x\) is ₹ 3000.
P's total investment is \(5000 \times 6 = 30\,000\) and Q's is \(8x\). Q's share of the profit is its share of the total investment:
\[ \begin{aligned} \frac{8x}{30\,000 + 8x} &= \frac{4}{9} \\ 72x &= 120\,000 + 32x \\ x &= 3000 \end{aligned} \]
Check: Q invests 24,000, P 30,000, and \(24\,000/54\,000 = 4/9\). 2500 gives Q only 20,000 (40%); 4687 and 8437 give Q more than 4/9.
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