Rahul gives a discount of x% after marking up the price by (3x + 10)%. Apart from it, he also uses a faulty balance which shows weight as 1050 gm, when it is actually 840 gm. By this he earns a profit of 64.69%. Find the value of x.

Using the faulty balance formula, overall profit percentage equals (100 + markup% - discount% - markup% * discount% / 100) * (false weight / true weight) - 100. Here, 64.69 equals (100 + 3x + 10 - x - x(3x + 10)/100) * (1050 / 840) - 100, which simplifies to 164.69 = (110 + 2x - 0.03x^2 - 0.1x) * 1.25. Testing x = 15, the right side becomes (110 + 30 - 6.75 - 1.5) * 1.25, which equals 131.75 * 1.25 to give 164.6875, matching the profit.

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