‘A’started a business with a capital of ₹54,000 and admitted ‘B’ and ‘C’ after 4 months and 6 months, respectively. At the end of the year, the profit was divided in the ratio 1 : 4 : 5. What is the difference between the capitals invested by ‘B’ and ‘C’?

Investment of A = ₹54,000
Time = 12 months
Let the investment of B and C be x and y respectively.
Time of the invest for B = 12 - 4 = 8 months
Time of the invest for C = 12 - 6 = 6 months
Profit share of A, B and C = 54000 $$\times 12 : x \times 8 : y \times 6 = 324000 : 4x : 3y
1 : 4 : 5 = 324000 : 4x : 3y
From first two,
1 : 4 = 324000 : 4x
x = 324000
Now
From first and third,
1 : 5 = 324000 : 3y
y = 540000
Difference between the capitals invested by ‘B’ and ‘C’ = 540000 - 324000 = Rs.216000