Mr. Ambani purchased a car of 3,00,000 and a bike for his son for 1,00,000. He sold the car at a profit of \[10\% \] and bike at a loss of \[20\% \]. What is the net gain or loss?
A. $2\%$ gain.
B. $1.5\%$ gain.
C. $2.5\%$ loss.
D. $2.5\%$ gain.
VerifiedHint: In this question we are asked to find the net gain of loss after selling the vehicles. Here we are given the amount of money spent on both the vehicles but we are not provided with the selling price, rather we know the respective gain and loss on selling the vehicles. So, we will make use of profit and loss percentage to find the net selling price and then find the overall gain or loss percentage.
Complete step-by-step answer:
We can find the selling price as \[SP = CP + \left( {CP \times \dfrac{{profit}}{{100}}} \right)\] in case of profit and \[SP = CP - \left( {CP \times \dfrac{{loss}}{{100}}} \right)\]in case of loss. (Where CP is the cost price of the product).
Step by step solution:
We are given that,
Mr. Ambani purchased a car for 3,00,000 and a bike for 1,00,000.
Therefore, cost price of car=3,00,000
Cost price of bike=1, 00,000
Total cost price=\[300000 + 100000 = 400000\].
Now, profit on car=\[10\% \]
So, the selling price of car
\[ = 300000 + \left( {300000 \times \dfrac{{10}}{{100}}} \right)\]
\[= 300000 + 30000\]
\[= 330000\]
SP of car = 3,30,000
Similarly, selling price of bike
\[ = 100000 - \left( {100000 \times \dfrac{{20}}{{100}}} \right)\]
\[ = 100000 - 20000\]
\[ = 80000 \]
SP of bike= 80,000
Now the total CP= 4,00,000
And total SP= 4,10,000.
Now we have both the total selling price and the cost price, so we can now find the net profit or loss.
We can see that net SP> net CP, there is a net profit, but we need to find the percentage of profit received by Mr. Ambani. For that first we calculate the net gain.
\[gain = SP - CP \]
\[= 410000 - 400000\]
\[= 10000 \]
Now, we find the gain percentage.
\[gain\,\,percentage = \dfrac{{gain \times 100}}{{CP}}\]
\[= \dfrac{{10000 \times 100}}{{400000}}\]
\[= 2.5\% \]
Therefore there is a gain of $2.5\%$.
Note: In this question there was a net gain at the end of the deal so we subtracted the total cost price from the selling price because the selling price was more than the cost price. But if there is net loss at the end then in that case the net cost price would be more than the net selling price. So in that case we will subtract the selling price from the cost price in order to determine the net loss and continue the question in the same way we did.
