Let the total amount invested by Anil, Bobby, and Chintu be $\text{‘I’}.$
Anil’s share of investment is $70\%.$ His share of profit decreases by ₹$ \; 420$ if the overall profit goes down from $18 \%$ to $15\%.$
Now, $70 \% \; \text{of} \; (18\% \; \text{of I} – 15\% \; \text{of I}) = 420$
$\Rightarrow 70 \% \; \text{of} \; 3\% \; \text{of I} = 420$
$\Rightarrow \frac{70}{100} \times \frac{3}{100} \times \text{I} = 420$
$\Rightarrow \boxed{\text{I} = 20000}$
Chintu’s share of profit increases by ₹$ \;80$ if the overall profit goes up from $15 \%$ to $17\%.$
Let the percentage share of Chintu be $\text{‘C’}.$
$\text{C} \% \; \text{of} \; 2\% \; \text{of I} = 80$
$\Rightarrow \frac{\text{C}}{100} \times \frac{2}{100} \times 20000 = 80$
$\Rightarrow \boxed{\text{C} = 20\%}$
Now, profit share by Bobby $ = 100\% – (70\% + 20\%)= 100\% – 90\% = 10\%$
$\therefore$ The amount invested by Bobby $ = 10\% \; \text{of I} = \dfrac{10}{100} \times 20000 =$ ₹ $\; 2000.$
Correct Answer $: \text{C}$