Question

A man purchases two clocks A and B at a total cost of Rs. 650. He sells A at 20% profit and B at a loss of 25% and gets the same selling price for both the clocks. What are the purchasing prices of A and B respectively?
a.Rs. 225, Rs. 425
b.Rs. 275, Rs. 375
c.Rs. 250, Rs. 400
d.Rs. 300, Rs. 350

Answer 1

Hint:Assume the cost of the clock A to be x. The cost of clock B will be Rs. 650-x. Now, calculate the selling price of clock A if the man gets a 20% profit. Similarly, calculate the selling price of clock B if the man gets a 25% loss. Now, it is given that the selling price of clock A is equal to the selling price of clock B. Solve it further and find the value of x. Using the value of x find the cost of clock B.

Complete step-by-step answer:
First of all, let us assume the cost of the clock A be Rs. x.
According to the question, it is given that the cost of clock A and B is Rs. 650.
The cost of the clock B = Rs. (650-x).
It is given that the man sells clock A at a profit of 20%.
The selling price of clock A = \[x+20\%\,of\,x=x+\dfrac{20}{100}x=\dfrac{6x}{5}\] ……………………..(1)
It is also given that the man sells clock B at a loss of 25%.
The selling price of clock B = \[\left( 650-x \right)-25\%\,of\,\left( 650-x \right)=\left( 650-x \right)-\dfrac{25}{100}\left( 650-x \right)=\left( 650-x \right)\left( 1-\dfrac{1}{4} \right)=\dfrac{(650-x)3}{4}\] …………..(2)
As per the information provided in the question, it is given that the man gets the same selling price for both the clocks.
Now, we have the same selling price for both of the clocks.
So, Selling price of clock A = selling price of clock B.
Now, from equation (1) and equation (2), we get
\[\begin{align}
  & \dfrac{6x}{5}=\dfrac{\left( 650-x \right)3}{4} \\
 & \Rightarrow \dfrac{24x}{3}=5\left( 650-x \right) \\
 & \Rightarrow 8x=650\times 5-5x \\
\end{align}\]
\[\begin{align}
  & \Rightarrow 8x+5x=650\times 5 \\
 & \Rightarrow 13x=650\times 5 \\
\end{align}\]
\[\Rightarrow x=\dfrac{650\times 5}{13}=50\times 5=250\] …………………………(3)
We have assumed that the cost of clock A is Rs. x.
The cost of clock A = Rs. 250.
The cost of the clock B = Rs. (650-x) = Rs. 400.
Hence, the correct option is C.

Note: In this type of question, one can make a mistake in percentage. It means one may forget to divide the percentage term by 100 during calculations. Like, 20% of x should be written as \[\dfrac{20}{100}\times x\] not as \[x\times 20\] . So, it should be remembered that we divide by 100 in percentage terms for removing the percentage sign.