A juice bar offers drinks in three different bottle sizes. The product of the prices (in Rs.) of the small, medium, and large bottles is Rs. 94,500. The prices of the small and large bottles are in the ratio 3:7. Later, the owner increases the price of the small bottle by Rs. 5 and that of the large bottle by Rs. 20, while keeping the medium bottle's price unchanged. As a result, the product of the new prices becomes Rs. 1,41,750. What is the sum of the original prices (in Rs.) of the three bottle sizes?

Let the original prices of the small and large bottles be 3x and 7x, respectively, and let the medium bottle's price be M. The first equation from the original product is 3x * M * 7x = 94500, which simplifies to 21x^2 * M = 94500. The second equation for the new prices is (3x + 5) * M * (7x + 20) = 141750. Dividing the second equation by the first gives (3x + 5)(7x + 20) / (21x^2) = 1.5. Solving this equation yields x = 10. The original prices are 30 for the small bottle, 70 for the large bottle, and 45 for the medium bottle, making their sum 145.

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