A, B and C started a business with their capitals in the ratio 1 : 4 : 4. At the end of every 3 months, A doubles his capital, B halves his capital and C leaves his capital unchanged. At the end ofthe year, if B’s share in the profit was ₹4,50,000, then the total profit(in ₹ lakhs) was

Capital ratio of the A, B and C = 1 : 4 : 4

Let the Capital of A, B and C be x, 4x and 4x respectively.

Capital for A for the 12 months = x, 2x, 4x, 8x

Capital for A for the 12 months = 4x, 2x, x, 0.5x

Capital for A for the 12 months = 4x, 4x, 4x, 4x

Profit ratio for the A, B and C = $$(\times 3) + (2x \times 3) + (4x \times 3) + (8x \times 3) : (4x \times 3) + (2x \times 3) + (x \times 3) + (0.5x \times 3) : (4x \times 12)$$

= 3x + 6x + 12x + 24x : 12x + 6x + 3x + 1.5x : 48x = 45x : 22.5x : 48x = 45 : 22.5 : 48

Total profit = 45 + 22.5 + 48 = 115.5 units

Profit share of B = 450000

22.5 unit = 450000

1 unit = 20000

Total profit = 20000 $$\times 115.5 = 2310000 = 23.1 lakh$$