Question

A motorcycle and a scooter were sold for Rs. 12000 each. The motorcycle was sold at a loss of 20% of the cost and the scooter at a gain of 20% of the cost. The entire transaction resulted in:
A. No loss or gain
B. Loss of Rs. 1000
C. Gain of Rs. 1000
D. Gain of Rs. 2000

Answer 1

Hint: First of all, we will find the formula for profit and loss and then find the amount for which the motor cycle and the scooter are bought. And then we will calculate the total cost price and compare it with the selling price. If we get that the cost price is less than the selling price, then we can say it as profit or else it is a loss.

Complete step-by-step answer:
So, now before proceeding with the solution we need to know what profit is and what loss is. After that we need to calculate the total cost price.
So, now we will find the total selling price. So, we can write,
Total selling price = selling price of motorcycle + selling price of scooter.
From the given data we have the selling price of motor cycle as Rs. 12000 and the selling price of scooter as Rs. 12000. So, we will get,
Total selling price = 12000 + 12000 = 24000
Now we need to find the cost price of a motorcycle and the scooter.
From the given data we can see that the motorcycle was sold at a loss of 20% of the cost.
Let the motor cycle be bought at a cost of Rs. A.
So, we know that the loss percentage is given by, $ \text{Loss percentage=}\dfrac{\left( \text{cost price} \right)-\left( \text{selling price} \right)}{\left( \text{cost price} \right)}\times 100 $
Now we have the selling price as Rs. 12000, the cost price as Rs. A and the loss percentage is 20%. So, on substituting these value in the equation we will get,
\[\dfrac{A-12000}{A}\times 100=20\]
On simplifying it further, we get,
 $ \dfrac{A-12000}{A}\times 100=20 $
On dividing both the sides by 100, we get,
 $ \dfrac{A-12000}{A}=\dfrac{20}{100} $
On multiplying both the sides with A, we get,
 $ A-12000=0.2A $
On taking 0.2A from the RHS to LHS and -12000 from LHS to RHS, we get,
 $ \begin{align}
  & A-0.2A=12000 \\
 & 0.8A=12000 \\
 & A=\dfrac{12000}{0.8} \\
 & A=15000 \\
\end{align} $
So, now the cost price of motorcycle is Rs. 15000
Now, let the scooter be bought at Rs. B
From the given data we have, the scooter sold at a gain of 20%
We know that, $ \text{Profit percentage=}\dfrac{\left( \text{selling price} \right)-\left( \text{cost price} \right)}{\left( \text{cost price} \right)}\times 100 $
So, now we have,
 $ \dfrac{12000-B}{B}\times 100=20 $
On dividing the whole equation by 100, we get,
 $ \dfrac{12000-B}{B}=\dfrac{20}{100} $
On multiplying the whole equation with B, we get,
 $ 12000-B=0.2B $
On taking -B from the LHS to RHS, we get,
 $ \begin{align}
  & 0.2B+B=12000 \\
 & 1.2B=12000 \\
 & B=\dfrac{12000}{1.2} \\
 & B=10000 \\
\end{align} $
So, now the cost price of a scooter is Rs. 10000.
So, now the total cost price is,
A + B = Rs. 15000 + Rs. 10000
= Rs. 25000
And we know that the total selling price is Rs. 24000.
So, now if we subtract the cost price from the selling price, we will get,
Selling price – Cost price
= Rs. 24000 – Rs. 25000
= - Rs. 1000
Here, ‘-‘ indicates that it is a loss. So, therefore it is a loss of Rs. 1000.
So the answer is option (B).

Note: There is a possibility that the students may make mistakes while calculating the cost price and so later on while calculating the profit or loss, it may result in errors. If we get a negative sign, it means it is a loss or else it is gain. Another mistake that the students may make is by taking the total selling price of the motor cycle and the scooter as Rs. 12000 instead of Rs. 24000. So, the students must do the calculations carefully.