Question

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

Answer 1

Hint: The given question revolves around the topic and concepts of profit and loss. The question deals with first purchasing some goods at a cost price, then selling portions of the goods at different prices and booking an overall profit of $ 10\% $ on the whole transaction. The loss percent at one of the two portions is given to us and we have to find the gain percent at the remaining portion so as to maintain the $ 10\% $ gain on the whole transaction.

Complete step by step solution:
The cost price of the goods is $ Rs\,380 $ .
Let the quantity of goods be x.
Then, the total amount spent in purchasing the goods is $ Rs\,380x $ .
Then, we are given that there is an overall profit of $ 10\% $ on the whole transaction.
So, we have to sell all the goods for $ 10\% $ profit collectively.
So, calculating $ 10\% $ on the cost price of $ Rs\,380x $ , we get,
 $ \Rightarrow \dfrac{{10}}{{100}} \times Rs\,380x $
Cancelling the common factors in numerator and denominator, we get,
 $ \Rightarrow Rs\,38x $
So, the collective profit on selling the goods is $ Rs\,38x $ .
So, the collective selling price is
  $ Rs\,380x + Rs\,38x = Rs\,418 $ .
Now, we are given that $ \dfrac{2}{3} $ rd of the goods are sold for a loss of $ 15\% $ . So, we get,
So, calculating $ 15\% $ loss on the cost price of $ Rs\,380 $ , we get,
 $ \Rightarrow \dfrac{{15}}{{100}} \times Rs\,380 $
Cancelling the common factors in numerator and denominator, we get,
 $ \Rightarrow \dfrac{3}{2} \times Rs\,38 $
 $ \Rightarrow Rs\,57 $
Now, there is a loss of $ Rs\,57 $ on selling the goods for a loss of $ 15\% $ .
So, the selling price for $ \dfrac{2}{3} $ rd of the goods is $ Rs380 - Rs\,57 = Rs323 $ .
Now, the collective selling price for $ \dfrac{2}{3} $ rd of the goods is
  $ Rs323 \times \dfrac{2}{3}x = Rs\dfrac{{646}}{3}x $ .
Now, the remaining goods have to be sold for
  $ Rs\,418 - Rs\dfrac{{646}}{3}x = Rs\,\dfrac{{1254 - 646}}{3}x = Rs\dfrac{{608}}{3}x $ .
So, the selling price for the rest $ \dfrac{1}{3} $ rd of the goods is $ Rs\dfrac{{608}}{3}x $ .
The cost price for rest $ \dfrac{1}{3} $ rd of the goods is $ Rs\,\dfrac{{380x}}{3} $ .
So, profit for rest $ \dfrac{1}{3} $ rd of the goods is
 $ Rs\dfrac{{608}}{3}x - Rs\,\dfrac{{380x}}{3} = Rs\dfrac{{228x}}{3} = Rs76x $
Now, we can calculate the gain percent for the rest $ \dfrac{1}{3} $ rd of the goods. So, we get,
 $ \Rightarrow Gain\% = \dfrac{{Rs76x}}{{\dfrac{{Rs380x}}{3}}} \times 100\% $
Simplifying the expression, we get,
 $ \Rightarrow Gain\% = \dfrac{{76 \times 3}}{{380}} \times 100\% $
Cancelling the common factors in numerator and denominator, we get,
 $ \Rightarrow Gain\% = 0.6 \times 100\% $
 $ \Rightarrow Gain\% = 60\% $
Hence, the remaining $ \dfrac{1}{3} $ rd of the goods have to be sold for $ 60\% $ so as to maintain a gain of $ 10\% $ on the whole transaction.
So, the correct answer is “ $ 60\% $ ”.

Note: One must have accuracy in arithmetic so as to solve these types of questions within a limited time frame. We should have a clear understanding of how to find the percentage of a specific number so as to find the gain and loss percent for the goods. One must have a strong grip over the concepts of profit and loss to understand these types of problems and solve them diligently.