Four partners, P, Q, R, and S, entered into a partnership to run a printing business. At the start of the year, P, Q, and R invested amounts that were in the ratio 2:3:4, and the sum of their three investments together came to Rs. 2,70,000. S did not join at the start like the other three partners; S joined a few months later and contributed an amount exactly one and a half times as large as Q's investment.

Since S joined late, S's investment remained active in the business for only a certain number of months, which is not directly stated, while P, Q, and R kept their investments running for the entire twelve months of the year. At the end of the year, the business earned a total profit of Rs. 1,98,000, and this profit was divided among the four partners strictly in proportion to the product of each partner's investment amount and the number of months that investment remained active. It is further known that the profit share received by R at the end of the year, compared to the profit share received by S at the end of the year, was in the ratio 4:3.