Question

Two friends P and Q started a business investing in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q's. At the end of the year, 20% of profit was earned, which was equal to Rs. 98000. Determine the amount invested by R ?

• A. Rs. 105000
• B. Rs. 420000
• C. Rs. 200000
• D. Rs. 110000
• E. Rs. 210000

Hint:

In partnership problems, the profit-sharing ratio is based on the product of investment and time. If the profit is given, work backwards to find the actual investment values.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
In partnership, profit is usually proportional to (Capital \( \times \) Time). The question implies the total investment relates to the percentage profit.
Step 2: Key Formula or Approach:
Total Investment \( \times \) Profit Rate \( = \) Profit Amount.
Step 3: Detailed Explanation:
Let the monthly investments be \( 5x, 6x, \) and \( 6x \) for P, Q, and R.
Investment units:
P: \( 5x \cdot 12 = 60x \)
Q: \( 6x \cdot 12 = 72x \)
R: \( 6x \cdot 6 = 36x \)
Total "Effective" Investment \( = 60x + 72x + 36x = 168x \).
The problem mentions a 20% profit on "average investment" per year (standard interpretation for this exam type).
Yearly Average Capital \( = 168x / 12 = 14x \).
\( 20% \) of \( 14x = 98000 \).
\( 2.8x = 98000 \Rightarrow x = 35000 \).
Amount invested by R \( = 6x = 6 \cdot 35000 = 210000 \).
Step 4: Final Answer:
The amount invested by R is Rs. 210,000.