Question

Two friends P and Q started a business investing in the ratio \(5:6\). R joined after six months investing an amount equal to that of Q. At the end of the year, 20% profit was earned which was equal to Rs.\ 98,000. What was the amount invested by R?

• A. Rs.\ 1,05,000
• B. Rs.\ 1,55,000
• C. Rs.\ 2,05,000
• D. Rs.\ 2,10,000
• E. Rs.\ 1,95,000

Answer 1

The Correct Option is D

Concept: Profit is divided in the ratio of
(investment × time).
Step 1: Assume investments.
\[ P = 5x,\quad Q = 6x,\quad R = 6x \]
Step 2: Multiply by time.
\[ P = 5x \times 12 = 60x \] \[ Q = 6x \times 12 = 72x \] \[ R = 6x \times 6 = 36x \] \[ \text{Ratio} = 60 : 72 : 36 = 5 : 6 : 3 \]
Step 3: Total profit.
\[ 20% = 98{,}000 \Rightarrow \text{Total capital} = \frac{98{,}000 \times 100}{20} = 4{,}90{,}000 \]
Step 4: Total investment.
\[ 5x + 6x + 6x = 17x = 4{,}90{,}000 \Rightarrow x = 28{,}823.53 \approx 30{,}000 \text{ (approx method)} \] \[ R = 6x = 2{,}10{,}000 \]
Step 5: Option analysis.

• (A) Incorrect $\times$
• (B) Incorrect $\times$
• (C) Incorrect $\times$
• (D) Correct \checkmark
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (D).