Question
Download Solution PDFP, Q and R enter into a partnership by investing their capitals in the ratio of
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Initial ratio of investments by P, Q, and R = 2/5 : 3/4 : 5/8
After 4 months, P increased his capital by 50% and Q decreased his capital by 20%
Total profit at the end of the year = ₹28,210
Formula used:
Share of profit = (Capital × Time) / Total Capital × Total Time
Calculation:
Let's convert the ratios to a common base for easier comparison:
P's initial investment = 2/5 = 16/40
Q's initial investment = 3/4 = 30/40
R's initial investment = 5/8 = 25/40
Total months = 12
For the first 4 months:
P's capital = 16 units, Q's capital = 30 units, R's capital = 25 units
For the next 8 months:
P increased his capital by 50% ⇒ New P's capital = 16 + 0.5 × 16 = 24 units
Q decreased his capital by 20% ⇒ New Q's capital = 30 - 0.2 × 30 = 24 units
R's capital remains the same = 25 units
Total investment in terms of units:
P's contribution = 16 × 4 + 24 × 8 = 256 units
Q's contribution = 30 × 4 + 24 × 8 = 312 units
R's contribution = 25 × 12 = 300 units
Total units = 256 + 312 + 300 = 868 units
Q's share of profit = (Q's units / Total units) × Total profit
⇒ Q's share = (312 / 868) × 28,210
⇒ Q's share = 10,140
∴ The correct answer is option 1.
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