# Mike sold two horses for Rs 18000 each. On one he got a profit of 20% and on the other he lost 20%. Find his total gain or loss.

Answer

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Hint: Here, we have to find the total selling price of the two horses and then compare it with the total cost price of those two horses to determine the net profit/loss.

Given, Cost price of each horse is ${\text{C}}{\text{.P.}} = 18000$

Profit percentage on selling first horse is $20\% $

Loss percentage on selling second horse is $20\% $

Since, \[{\text{Amount of profit or loss}} = \dfrac{{{\text{Profit or loss percentage}}}}{{100}} \times \left( {{\text{C}}{\text{.P}}} \right)\]

Amount of profit gained by selling first horse = $\dfrac{{20}}{{100}} \times \left( {18000} \right) = {\text{Rs }}3600$

Amount of loss occurred by selling second horse = $\dfrac{{20}}{{100}} \times \left( {18000} \right) = {\text{Rs }}3600$

Also we know that when profits occurs, ${\text{S}}{\text{.P.}} = {\text{C}}{\text{.P.}} + {\text{Amount of profit gained}}$

and when loss occurs, ${\text{S}}{\text{.P.}} = {\text{C}}{\text{.P.}} - {\text{Amount of loss occurred}}$

Using above formulas, we can write

For selling the first horse (profit occurs), ${\left( {{\text{S}}{\text{.P.}}} \right)_1} = 18000 + 3600 = {\text{Rs 21600}}$

For selling the second horse (loss occurs), ${\left( {{\text{S}}{\text{.P.}}} \right)_2} = 18000 - 3600 = {\text{Rs }}14400$

Now, Total cost price of two horses is ${\left( {{\text{C}}{\text{.P.}}} \right)_{\text{T}}} = 2 \times \left( {{\text{Cost price of each horse}}} \right) = 2 \times 18000 = {\text{Rs }}36000$

Total selling price of two horses is ${\left( {{\text{S}}{\text{.P.}}} \right)_{\text{T}}} = {\left( {{\text{S}}{\text{.P.}}} \right)_1} + {\left( {{\text{S}}{\text{.P.}}} \right)_2} = 21600 + 14400 = {\text{Rs 36000}}$

Clearly, we can see that the selling price of the two horses is equal to the cost price of those two horses which indicates in total there is neither profit nor loss.

So, Mike has gained or lost nothing.

Note: In these types of problems, the total cost price of all the items is compared with the total selling price of all the items. If the selling price is higher than the cost price, then profit occurs and if the cost price is higher than selling price then loss has occurred and if both selling price and cost price are equal then neither profit nor loss occurs.

Given, Cost price of each horse is ${\text{C}}{\text{.P.}} = 18000$

Profit percentage on selling first horse is $20\% $

Loss percentage on selling second horse is $20\% $

Since, \[{\text{Amount of profit or loss}} = \dfrac{{{\text{Profit or loss percentage}}}}{{100}} \times \left( {{\text{C}}{\text{.P}}} \right)\]

Amount of profit gained by selling first horse = $\dfrac{{20}}{{100}} \times \left( {18000} \right) = {\text{Rs }}3600$

Amount of loss occurred by selling second horse = $\dfrac{{20}}{{100}} \times \left( {18000} \right) = {\text{Rs }}3600$

Also we know that when profits occurs, ${\text{S}}{\text{.P.}} = {\text{C}}{\text{.P.}} + {\text{Amount of profit gained}}$

and when loss occurs, ${\text{S}}{\text{.P.}} = {\text{C}}{\text{.P.}} - {\text{Amount of loss occurred}}$

Using above formulas, we can write

For selling the first horse (profit occurs), ${\left( {{\text{S}}{\text{.P.}}} \right)_1} = 18000 + 3600 = {\text{Rs 21600}}$

For selling the second horse (loss occurs), ${\left( {{\text{S}}{\text{.P.}}} \right)_2} = 18000 - 3600 = {\text{Rs }}14400$

Now, Total cost price of two horses is ${\left( {{\text{C}}{\text{.P.}}} \right)_{\text{T}}} = 2 \times \left( {{\text{Cost price of each horse}}} \right) = 2 \times 18000 = {\text{Rs }}36000$

Total selling price of two horses is ${\left( {{\text{S}}{\text{.P.}}} \right)_{\text{T}}} = {\left( {{\text{S}}{\text{.P.}}} \right)_1} + {\left( {{\text{S}}{\text{.P.}}} \right)_2} = 21600 + 14400 = {\text{Rs 36000}}$

Clearly, we can see that the selling price of the two horses is equal to the cost price of those two horses which indicates in total there is neither profit nor loss.

So, Mike has gained or lost nothing.

Note: In these types of problems, the total cost price of all the items is compared with the total selling price of all the items. If the selling price is higher than the cost price, then profit occurs and if the cost price is higher than selling price then loss has occurred and if both selling price and cost price are equal then neither profit nor loss occurs.

Last updated date: 21st Sep 2023

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