In a partnership firm, A invests \(\frac{1}{6}\)th of the total invest

B’s investment $I_B = \frac{1}{3} I$. B’s tenure $T_B = \frac{1}{3} T$.
B’s profit share is proportional to $I_B \times T_B = (\frac{1}{3} I) \times (\frac{1}{3} T) = \frac{1}{9} IT$.

C invests the remaining part of the investment for the full duration.
C’s investment $I_C = \text{Total Investment} – I_A – I_B$.
$I_C = I – \frac{1}{6} I – \frac{1}{3} I = I – (\frac{1}{6} + \frac{2}{6}) I = I – \frac{3}{6} I = I – \frac{1}{2} I = \frac{1}{2} I$.
C’s tenure $T_C = T$ (full duration).
C’s profit share is proportional to $I_C \times T_C = (\frac{1}{2} I) \times T = \frac{1}{2} IT$.

The ratio of the profit shares of A, B, and C is the ratio of their (Investment $\times$ Time) products:
Ratio = $\frac{1}{36} IT : \frac{1}{9} IT : \frac{1}{2} IT$.
Dividing by $IT$ (assuming $I, T > 0$):
Ratio = $\frac{1}{36} : \frac{1}{9} : \frac{1}{2}$.
To simplify this ratio, multiply by the Least Common Multiple (LCM) of the denominators (36, 9, 2), which is 36.
Ratio = $36 \times \frac{1}{36} : 36 \times \frac{1}{9} : 36 \times \frac{1}{2}$
Ratio = $1 : 4 : 18$.

The sum of the ratio parts is $1 + 4 + 18 = 23$.
The total profit is ₹46,00,000.
C’s share of the profit is the total profit multiplied by C’s ratio part divided by the sum of ratio parts.
C’s share = $\frac{18}{23} \times ₹46,00,000$.
$\frac{46,00,000}{23} = 2,00,000$.
C’s share = $18 \times ₹2,00,000 = ₹36,00,000$.