If goods be purchased for Rs.450 and 1/3 is sold at a loss of 10%. At what gain % should the remainder is sold to has to gain 20% on the whole transaction?

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Solution

Cost Price of ${\frac{1}{3}}^{r d}$ of goods = $\frac{1}{3} \times 450 = R S .150$
Selling Price of ${\frac{1}{3}}^{r d}$ of goods = $150 \times \frac{90}{100} = R s . 135$ [10% loss]
The total selling price with 20% gain should be $450 \times \frac{120}{100} = R s . 540$
Therefore, the selling price of the remaining ${\frac{2}{3}}^{r d}$ of the goods should be 540-135= Rs. 405
The cost price of the remaining ${\frac{2}{3}}^{r d}$ of the goods is Rs. 300.
Therefore, Gain % = $\frac{405 - 300}{300} \times 100 = 35$ %
Thus, the remaining ${\frac{2}{3}}^{r d}$ of the goods must be sold at 35% gain so as to get 20% gain in the whole transaction.

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