Question

Manoj travels from Meerut to Delhi to buy goods which he gets $10\%$ cheaper in Delhi than in Meerut. If his journey expenses are Rs. 160 and he earns Rs. 240 by selling goods at Meerut; calculate the price of the goods, he paid at Delhi.

Answer 1

Hint: We assume the original marked price of the good at Delhi which also the same everywhere. We find the cost price of the good only which Manoj paid at Delhi. Then we add the journey expenses to get the whole expense. After selling the goods at Meerut we get the algebraic equation with the help of the gain he got. We solve the equation to find the original price and the solution to the problem.

Complete step-by-step solution:
Let the original Marked price at Delhi and Selling price at Meerut both be RS. x.
The price of goods is the same everywhere. He got a $10\%$ discount in Delhi.
After $10\%$ discount, Manoj buys it for $x\left( 1-\dfrac{10}{100} \right)$ Rs which is equal to $0.9x$.
His journey expenses are Rs. 160. That will add up as his cost price in calculating his gain.
Total cost price which he bears is $\left( 0.9x+160 \right)$ Rs.
He earns Rs. 240 by selling goods at Meerut. That was his profit. He sold the goods in x Rs.
So, selling price -cost price =gain
We construct the equation in its algebraic form and get
$x-\left( 0.9x+160 \right)=240$
Now we solve it to find the value of x.
\[\begin{align}
  & x-\left( 0.9x+160 \right)=240 \\
 & \Rightarrow x-0.9x-160=240 \\
 & \Rightarrow 0.1x=400 \\
 & \Rightarrow x=\dfrac{400}{0.1}=4000 \\
\end{align}\]
So, the original price of the goods is 4000.
We need to find the price he paid in Delhi.
The price paid by Manoj at Delhi $0.9x$ which is equal to $0.9\times 4000=3600$ Rs.
So, Manoj paid Rs. 3600 in Delhi.

Note: We need to remember that although the journey expenses are not related to goods price, it has to be considered when we are formulating the relation as the gain is only possible when all the expenses have been covered by it. We need to be careful that we need to find the price Manoj paid at Delhi which was less than the original marked price.