Question

A Shopkeeper mixes varieties of Tea, one costing Rs.40/kg and another Rs.50/kg in the ratio 3:2, if he sells the mixed variety of tea at Rs.48/kg, his gain or loss percent is
A. 48.4% gain
B. 48.4% loss
C. 10% gain
D. 10% loss

Answer 1

Hint: We will first find out the cost Price of the mixed tea with the help of information given in the question. And then we will determine the profit or loss on the basis of selling Price and cost Price of the tea. The profit/loss will be calculated in percentage as follows:
\[{\rm{\% profit/loss}}\,\, = \,\,\dfrac{{proft/loss}}{{{\rm{cost Price}}}} \times 100\]

Complete step-by-step answer:
In this question, first we have to find out the cost Price of 1kg of mixed tea. To do this, we will make use of the data given in question. It is given in the question that 3 parts of the mixed tea is coming from the tea which has cost Rs.40/kg and 2 parts of the tea are coming from the tea which has cost Rs.50/kg. Thus, we can say that the 3/5 part of the mixed tea is Rs 40/kg and 2/5 part of the tea is Rs 50/kg. Thus, the total cost Price of the mixed tea is obtained by adding both. Thus, we get following cost Price of mixed tea:
\[{\rm{Cost Price = }}\,\dfrac{3}{5}\, \times 40\, + \dfrac{2}{5}\, \times \,50\]
\[ \Rightarrow {\rm{Cost Price = }}\,\dfrac{{120}}{5}\,\, + \dfrac{{100}}{5}\]
\[ \Rightarrow {\rm{Cost Price = }}\,\dfrac{{120 + 100}}{5}\]
\[ \Rightarrow {\rm{Cost Price = }}\,\dfrac{{220}}{5}\]
\[ \Rightarrow {\rm{Cost Price = }}\,Rs.44{\rm{/kg}}\]
Now, we have calculated the cost Price of the mixed tea. As we can clearly see that the cost Price of the mixed tea is less than the selling Price of mixed tea, the shopkeeper will get profit. The amount of profit will be calculated by the formula:
 \[{\rm{Profit = }}\,\,{\rm{Selling Price}}\,{\rm{ - }}\,{\rm{Cost Price}}\]
\[ \Rightarrow \,\,\,{\rm{Profit = }}\,\,Rs.48\, - \,Rs.44\]
\[ \Rightarrow \,\,\,{\rm{Profit = }}\,\,Rs.4/kg\]
Now we have to calculate the percentage of profit/gain. The formula to do this is given as:
\[{\rm{\% profit }}\,{\rm{ = }}\dfrac{{{\rm{profit}}}}{{{\rm{cost Price}}}}\, \times \,100\]
\[ \Rightarrow \,\,\,\,\,\,\,\,{\rm{\% profit }}\,{\rm{ = }}\dfrac{{\rm{4}}}{{{\rm{44}}}}\, \times \,100\]
\[ \Rightarrow \,\,\,\,\,\,\,\,{\rm{\% profit }}\,{\rm{ = }}\dfrac{{\rm{1}}}{{11}}\, \times \,100\]
\[ \Rightarrow \,\,\,\,\,\,\,\,{\rm{\% profit }}\,{\rm{ = }}9.09\% \]
\[ \Rightarrow \,\,\,\,\,\,\,\,{\rm{\% profit }}\,{\rm{ = }}10\% \]
Hence, option (c) is correct.


Note: The cost Price can also be calculated as follows:
 Let the value of one part be x, then we will get
\[{\rm{3x + 2x}}\,{\rm{ = }}\,{\rm{1kg}}\]
\[ \Rightarrow \,\,\,{\rm{5x}}\,{\rm{ = }}\,{\rm{1kg}}\]
\[ \Rightarrow \,\,\,\,\,{\rm{x}}\,{\rm{ = }}\,\dfrac{{\rm{1}}}{5}{\rm{kg}}\]

We get the amount of \[{\rm{3}}\,{\rm{x = }}\dfrac{3}{5}\]kg and \[{\rm{2}}\,{\rm{x}}\,{\rm{ = }}\,\dfrac{2}{5}\]kg. When we will multiply them with their respective values, we will get cost Price as
\[Cost{\rm{ Price}}\,{\rm{ = }}\,\left( {3x\, \times \,40} \right)\, + \,\left( {2x\, \times \,50} \right)\]
\[Cost{\rm{ Price}}\,{\rm{ = }}\,\left( {\dfrac{3}{5}\, \times \,40} \right)\, + \,\left( {\dfrac{2}{5}\, \times \,50} \right)\]
\[Cost {\rm{ Price}}\,{\rm{ = }}\,\dfrac{{220}}{5}\, = \,Rs.44/kg\]