Three persons p, q, r have to divide a certain sum of money in the ratio 2 : 3 : 5, but they divide it in the ratio 3 : 4 : 5. As a result q gets $30 extra. What is the total amount divided?

Let the total amount divided be x. According to the initial ratio of 2 : 3 : 5, q's intended share was 3/10 of x, and according to the actual ratio of 3 : 4 : 5, q's received share was 4/12 (or 1/3) of x. The difference is 1/3 of x minus 3/10 of x, which equals x/30, and this equals 30. Solving x/30 = 30 gives x = 900.

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