Raj invested Rs. 76,000 in a business. After few months Monty joined him and invested Rs. 57,000. At the end of the year, both of them shared the profits in the ratio of 2 : 1. After how many months did Monty join Raj?

Using the partnership formula, the ratio of profits equals the ratio of the product of their investments and time periods, so 76000 * 12 divided by 57000 * x equals 2. Solving the equation 912000 divided by 57000x equals 2 gives 16 divided by x equals 2, which means x equals 8. Since Monty's money was invested for 8 months, he joined the business after 12 minus 8, which is 4 months.

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