Question

# If Sohan while selling two goats at the same price, makes a profit of 10% on one goat and suffers a loss of 10% on the other oneA ) He makes no profit and no lossB ) He makes a profit of 1%C ) He suffers a loss of 1%D ) He suffers a loss of 2%

Hint: Find out the total cost price and selling price by assuming the cost price of anyone goat to be 100. Use the standard formulae of loss and profit percentage to solve the question.

Complete step by step solution: It has been given that Sohan makes a profit of 10% on selling one goat and a loss of 10% on selling the second goat at the same selling price. This implies that the cost price of both goats is different.
Let us assume that the cost price of the goat on which he makes a profit of 10% be 100.
We know that $S.P = C.P \times \dfrac{{\left( {100 + profit\% } \right)}}{{100}}$
Thus, we get the selling price of this goat to be equal to
$100 \times \dfrac{{\left( {100 + 10} \right)}}{{100}} = 110$
Since the selling price of both the goats are the same, the selling price of the goat sold at a loss of 10% is also 110.
We know that $C.P = S.P \times \dfrac{{100}}{{\left( {100 - loss\% } \right)}}$

Thus, we get the cost price of the goat sold at a loss of 10% to be equal to
$\dfrac{{100}}{{\left( {100 - 10} \right)}} \times 110 = \dfrac{{1100}}{9}$
Thus, the total cost price of both the goats is equal to
$100 + \dfrac{{1100}}{9} = \dfrac{{2000}}{9}$
We know that the total selling price is equal to
$2 \times 110 = 220$
Since the total cost price $\dfrac{{2000}}{9}$is greater than the total selling price $220$ , Soham makes a overall loss of
$\dfrac{{2000}}{9} - 220 = \dfrac{{20}}{9}$
We know that $loss\% = \dfrac{{loss}}{{C.P}} \times 100$
Thus, we get the loss percent to be equal to
$\dfrac{{\dfrac{{20}}{9}}}{{\dfrac{{2000}}{9}}} \times 100 = \dfrac{{20}}{{2000}} \times 100 = 1\%$
Thus, he suffers a total loss of 1%.

Note: In such type of questions, it is advisable to assume anyone cost price to be equal to 100 to make our calculation easier in using profit percentage formula: The profit percentage can be calculated as Profit % = 100 × Profit/Cost Price. Percentage Loss: The loss percentage can be calculated as; Loss % = 100 × Loss/Cost Price.