Questions & Answers

Question

Answers

A ) He makes no profit and no loss

B ) He makes a profit of 1%

C ) He suffers a loss of 1%

D ) He suffers a loss of 2%

Answer
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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%.