If goods be purchase for Rs.$380$ and $\dfrac {2}{3}$rd be sold at loss of 15%, at what gain percent should the remainder be sold so as to gain $10$% on the whole transaction

Using the method of balancing overall profit or loss, the ratio of parts sold is (2/3) to (1/3), which simplifies to a 2 to 1 ratio. The target overall gain is 10%, and the first part is sold at a 15% loss (-15). Applying the weighted average formula (2 x -15) + (1 x y) = 3 x 10, we solve -30 + y = 30. This yields y = 60, meaning the remaining part must be sold at a 60% gain.

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