"Rittu and Mittu started a cosmetic business with Rittu investing Rs. 30,000 and Mittu investing a certain amount of money. They hired a receptionist as a manager and agreed to pay him a 10% commission on the total profit. After one year, they offered the receptionist the opportunity to become a partner by contributing Rs. 40,000. Over two years, the business accumulated a total profit of Rs. ____. The difference between the total amount received by the receptionist (including profit and commission) and Mittu's share of the profit at the end of two years is Rs. ____. Now, you need to find the missing values in the blanks."

"Which set of values, from the following options, can be placed in the blanks in the same order as listed to make the statement true:

I. 40,000, 2,00,000, 20,000

II. 30,000, 3,00,000, 7,500

III. 60,000, 2,20,000, 50,000

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.