Rittu and Mittu started a cosmetic business with Rittu

Solution

ATQ, For case I: Ratio of profit shares of 'Rittu', 'Mittu' and 'Receptionist' at the end of two years = (30000 × 2):(40000 × 2):(40000 × 1) = 3:4:2 So, commission of 'Receptionist' = 2,00,000 × 0.1 = Rs. 20,000 So, gross profit remaining to distribute = 200000 - 20000 = Rs. 1,80,000 So, profit share of 'Mittu' = 1,80,000 × (4/9) = Rs. 80,000 So, profit share of 'Receptionist' = 1,80,000 × (2/9) = Rs. 40,000 So, required difference = 80000 - (40000 + 20000) = Rs. 20,000 So, case I is true. For Case II: Ratio of profit shares of 'Rittu', 'Mittu' and 'Receptionist' at the end of two years = (30000 × 2):(30000 × 2):(40000 × 1) = 3:3:2 So, commission of 'Receptionist' = 3,00,000 × 0.1 = Rs. 30,000 So, gross profit remaining to distribute = 300000 - 30000 = Rs. 2,70,000 So, profit share of 'Mittu' = 2,70,000 × (3/8) = Rs. 1,01,250 So, profit share of 'Receptionist' = 2,70,000 × (2/8) = Rs. 67,500 So, required difference = 101250 - (67500 + 30000) = Rs. 3,750 So, case II is not true. For case III: Ratio of profit shares of 'Rittu', 'Mittu' and 'Receptionist' at the end of two years = (30000 × 2):(60000 × 2):(40000 × 1) = 3:6:2 So, commission of 'Receptionist' = 2,20,000 × 0.1 = Rs. 22,000 So, gross profit remaining to distribute = 220000 - 22000 = Rs. 1,98,000 So, profit share of 'Mittu' = 1,98,000 × (6/11) = Rs. 1,08,000 So, profit share of 'Receptionist' = 1,98,000 × (2/11) = Rs. 36,000 So, required difference = 108000 - (36000 + 22000) = Rs. 50,000 So, case III is true.