Question

Pooja sold two of her cars for 350000/- each. On one, she made a profit of \[25\%\] and on the other a loss of \[20\%\] . Find her overall gain or loss.
(a) Loss of 18000/-
(b) Gain of 38000/-
(c) Gain of 42000/-
(d) Loss of 17500/-

Answer 1

Hint: We solve this problem by using the simple formula of gain and loss percentage. If C.P is the cost price and S.P is the selling price then
 \[\begin{align}
  & \text{gain percentage}=\dfrac{S.P-C.P}{C.P}\times 100 \\
 & \text{Loss percentage}=\dfrac{C.P-S.P}{C.P}\times 100 \\
\end{align}\]
By using these formulas we find the cost prices of each car and then we find combined loss or gain.

Complete step by step answer:
Let us solve for the first car.
We are given that the car is sold for 350000/-.
So we can take the selling price as
 \[\Rightarrow S.P=350000\]
Let us assume the cost price of the first car as \[{{\left( C.P \right)}_{1}}\] .
We are given that there is a gain of \[25\%\] on the first car.
We know that the formula for gain percentage is given as
 \[\text{gain percentage}=\dfrac{S.P-C.P}{C.P}\times 100\]

By substituting the required parameters in above formula we get
 \[\begin{align}
  & \Rightarrow 25=\dfrac{350000-{{\left( C.P \right)}_{1}}}{{{\left( C.P \right)}_{1}}}\times 100 \\
 & \Rightarrow \dfrac{1}{4}=\dfrac{350000-{{\left( C.P \right)}_{1}}}{{{\left( C.P \right)}_{1}}} \\
\end{align}\]
By cross multiplying and taking similar terms on same side we get
 \[\begin{align}
  & \Rightarrow {{\left( C.P \right)}_{1}}=1400000-4{{\left( C.P \right)}_{1}} \\
 & \Rightarrow {{\left( C.P \right)}_{1}}=\dfrac{1400000}{5} \\
 & \Rightarrow {{\left( C.P \right)}_{1}}=280000 \\
\end{align}\]
Therefore the cost price of the first car is 280000/-.
Now, let us consider the second car.
We are given that the car is sold for 350000/-.
So we can take the selling price as
 \[\Rightarrow S.P=350000\]
Let us assume that the cost price of the second car is \[{{\left( C.P \right)}_{2}}\] .
We are given that there is a loss of \[20\%\] on the first car.
We know that the formula for loss percentage is given as
 \[\text{Loss percentage}=\dfrac{C.P-S.P}{C.P}\times 100\]
By substituting the required parameters in above formula we get
 \[\begin{align}
  & \Rightarrow 20=\dfrac{{{\left( C.P \right)}_{2}}-350000}{{{\left( C.P \right)}_{2}}}\times 100 \\
 & \Rightarrow \dfrac{1}{5}=\dfrac{{{\left( C.P \right)}_{2}}-350000}{{{\left( C.P \right)}_{2}}} \\
\end{align}\]
By cross multiplying and taking similar terms on same side we get
 \[\begin{align}
  & \Rightarrow {{\left( C.P \right)}_{2}}=5{{\left( C.P \right)}_{2}}-1750000 \\
 & \Rightarrow {{\left( C.P \right)}_{2}}=\dfrac{1750000}{4} \\
 & \Rightarrow {{\left( C.P \right)}_{2}}=437500 \\
\end{align}\]
Therefore the cost price of the first car is 437500/-.
Now the total cost price of two cars is
 \[\begin{align}
  & \Rightarrow C.P={{\left( C.P \right)}_{1}}+{{\left( C.P \right)}_{2}} \\
 & \Rightarrow C.P=280000+437500 \\
 & \Rightarrow C.P=717500 \\
\end{align}\]
Now the total selling price of two cars is
 \[\begin{align}
  & \Rightarrow S.P=350000+350000 \\
 & \Rightarrow S.P=700000 \\
\end{align}\]
Here, we can see that the selling price is less than the cost price.
So, there is a loss. This loss is calculated as
 \[\begin{align}
  & \Rightarrow \text{Loss}=C.P-S.P \\
 & \Rightarrow \text{Loss}=717500-700000 \\
 & \Rightarrow \text{Loss}=17500 \\
\end{align}\]
Therefore, there is a loss of 17500/- for both cars.

So, the correct answer is “Option d”.

Note: Students may make mistakes in taking the gain or loss percentage formula. There are two different formulas for each gain and loss percentage.
 \[\begin{align}
  & \text{gain percentage}=\dfrac{S.P-C.P}{C.P}\times 100 \\
 & \text{Loss percentage}=\dfrac{C.P-S.P}{C.P}\times 100 \\
\end{align}\]
But students may consider there is only one formula and proceed for a solution which in turn results in a negative value of cost price which is impossible. So, the formulas should be remembered and the calculations part has to be taken care of.