A and B started a business with some amount ratio of 2 : 1. After some months they double their share and after 2 months, B leaves the business and C joined the business with an amount Rs. 10000. After 4 months of joining, C doubles his money, and B comes back to the business with his initial principal Rs. 2000. At the end of the year, it is seen that the share of A and C are the same. After how many month A and B double their amount? Correct Answer 4 Months Given: A and B started the business with a certain amount at the ratio 2 : 1 After some month they double their money. After that of 2 months, B leave business and C joined with Rs. 10000 After 4 months of joining C double his money and B back to the business with his initial money Rs. 2000 At the end of the year share of A and C are same. Concept Used: Concept of partnership and ratio Calculation: At the end of the year share of A and C are same. That means at the end of the year the ratio of the share of A and C will be the same It is given that B joined the business again with his initial money Rs. 2000 and at the beginning ratio of money of A and B was 2 : 1 That means at the beginning share of A was Rs.4000 Let, after x months A and B Double their money In x month share of A became 4000x After x month A double his money and there was no further change That means the share of A for (12 – x) months is (12 – x) × 8000 Total share of A is {4000x + (12 – x) × 8000} ⇒ (4000x + 12 × 8000 – 8000x) ⇒ (12 × 8000 – 4000x) ----(1) C joined the business with Rs. 10000 and continue it for 4 months After 4 months he doubles his money for the rest of the year C’s money was Rs. 20000 for Total share of C is ⇒ (40000 + 120000 – 20000x) ⇒ (160000 – 20000x) ----(2) From (1) and (2) get, (12 × 8000 – 4000x) = (160000 – 20000x) ⇒ 96000 – 4000x = 160000 – 20000x ⇒ 16000x = 64000 ⇒ x = 4 ∴ After 4 months A and B double their money.