A started a business with a capital of Rs. 54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided among the three in the ratio 1 : 4 : 5. What is the sum (in Rs.) of the capitals invested by B and C?

\[\begin{array}{*{20}{c}} {}&{\text{A}}&:&{\text{B}}&:&{\text{C}} \\ {{\text{Profit}} \to }&1&:&4&:&5 \\ {{\text{Duration}} \to }&{12}&:&8&:&6 \\ {{\text{Investment}} \to }&{\frac{1}{{12}}}&:&{\frac{4}{8}}&:&{\frac{5}{6}} \\ {}&2&:&{12}&:&{20} \end{array}\]
$${\text{Investment}} \to \frac{{{\text{Profit}}}}{{{\text{Duration}}}}$$
Investment by B and C = 12 + 20 = 32 units
2 units → 54,000
1 unit → 27,000
32 units → 32 × 27,000 = 8,64,000
Sum of investment by B and C = Rs. 8,64,000