'Aman,' 'Bheema,' and 'Ritika' initiated a business by investing Rs. 400, Rs. 500, and Rs. 900, respectively. After __ months from the start of the business, 'Ritika' withdrew all of her investment. 'Aman' increased his investment by __% after 6 months from the start of the business. The annual profit share of 'Bheema' is (1/3)rd of the total profit earned from the business. The blanks can be correctly filled using the values provided in which of the following statements?
I. 6, 75%
II. 8, 20%
III. 5, Rs. 450

ATQ, From I: Ratio of profit shares of ‘Aman’, ‘Bheema’ and ‘Ritika’, respectively = (400 × 6 + 400 × 1.75 × 6):(500 × 12):(900 × 6) = (2400 + 4200):(6000):(5400) = 11:10:9 So, profit share of ‘Bheema’ out of total profit = 10 ÷ (11 + 10 + 9) = (1/3) So, I is true. From II: Ratio of profit shares of Aman’, ‘Bheema’ and ‘Ritika’, respectively = (400 × 6 + 400 × 1.2 × 6):(500 × 12):(900 × 8) = (2400 + 2880):(6000):(7200) = 22:25:30 So, profit share of ‘Bheema’ out of total profit = 25 ÷ (22 + 25 + 30) = (25/77) ≠ (1/3) So, II is false. From III: Ratio of proit shares of Aman’, ‘Bheema’ and ‘Ritika’, respectively = (400 × 6 + (400 + 450) × 6):(500 × 12):(900 × 5) = (2400 + 5100):(6000):(4500) = 5:4:3 So, proit share of ‘Bheema’ out of total proit = 4 ÷ (5 + 4 + 3) = (4/12) = (1/3) So, Ill is true.