A, B and C started a business with investments of Rs.24000, Rs.45000 and Rs.63000 respectively and they invested the amounts for (x + 4) months, x months and 2x months respectively. If the profit share of A is 19/22 less than the total profit, find the value of [(x + 26) ÷ 2].

ATQ, The ratio of the profit share of A, B and C = [24000 * (x + 4)] : [45000 * x] : [63000 * (2x)] = [24 * (x + 4)] : [45x] : [126x] = [8 * (x + 4)] : 15x : 42x = (8x + 32) : 15x : 42x Total profit share = (8x + 32) + 15x + 42x = 65x + 32 The profit share of A / Total profit: A’s share is 19/22 less than the total profit ⇒ A’s share / Total profit = (22 – 19)/22 = 3/22 So, (8x + 32) / (65x + 32) = 3/22 Cross-multiplying, 22(8x + 32) = 3(65x + 32) 176x + 704 = 195x + 96 704 – 96 = 195x – 176x 608 = 19x x = 608 / 19 = 32 Required value = (x + 26) ÷ 2 = (32 + 26) ÷ 2 = 58 ÷ 2 = 29