Question

A trader purchased a wall clock and a watch for a sum of Rs.5070. He sold them making a profit of 10% on the wall clock and 15% on the watch. He earns a profit of Rs.669.50. Find the cost price of the wall clock and that of the watch.

Answer 1

Hint: Suppose, the cost of a wall clock is Rs.x, then the cost of watch would become Rs.(5070-x), because the total of both of them is Rs.5070. Putting these values as cost price in the profit % formula, given by \[\text{Profit }\!\!\%\!\!\text{ = }\dfrac{\text{SP-CP}}{Cp}\times 100\] selling price of the wall clock and the watch could be found out as we are given the profit % of both.

Complete step by step answer:
A trader purchases a wall clock and a watch. The total cost of these two items is Rs.5070
Let us take the price of one wall clock as Rs.x, then the price of one watch will be Rs. (5070-x)
After buying the items, the trader sells them earning profit. It means he is selling the items at a cost higher than the cost he bought them.
Profit % earned on the wall clock is 10.
We know how to calculate the profit%. We will use the below formula to calculate,
\[\text{Profit }\!\!\%\!\!\text{ = }\left( \dfrac{\text{Selling Price-Cost Price}}{\text{Cost Price}} \right)\times 100\]
Cost price of wall clock is 'x'
Profit % is 10
Putting these values in the formula stated above, we get
\[10=\left( \dfrac{SP-x}{x} \right)\times 100\text{ }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. (1)}\]
Now, profit earned on watch is 15%
Cost price of 1 watch is Rs.(5070-x)
Suppose that, selling price of 1 watch is $SP'$, then, putting these values in formula stated earlier, we get
\[15=\dfrac{SP'-\left( 5070-x \right)}{\left( 5070-x \right)}\times 100\text{ }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. (2)}\]
We are given with one more important information, that, the total profit not the profit % in Rs is Rs.699.50
Since, \[\text{Profit = Selling price - Cost price }\Rightarrow \text{ SP-CP}\]
From equation (1) and (2) we get,
\[\begin{align}
  & SP-CP=\dfrac{10}{100}\times \left( x \right) \\
 & SP'-CP'=\dfrac{15}{100}\times \left( 5070-x \right) \\
\end{align}\]
Addition of these two equation would lead to the total profit earned in Rs, we get
\[\begin{align}
  & \dfrac{10x}{100}+\dfrac{15\left( 5070-x \right)}{100}=Rs.699.50 \\
 & \Rightarrow 0.1x+760.5-0.15x=699.50 \\
 & \Rightarrow -0.05x+760.5=699.50 \\
 & \Rightarrow 0.05x=61 \\
 & \Rightarrow x=1220 \\
\end{align}\]
The cost price of the wall clock was x i.e. x = Rs.1220
The cost price of the watch was (5070-x) i.e. Rs.3850

Note: This question can also be directly solved by adding the 10% of the cost price of the wall clock, which is assumed as x and 15% of the cost price of watch, which is (5070-x) and then taking the sum of these to be Rs.699.50.
Therefore, we will get the equation as, \[\dfrac{10x}{100}+\dfrac{15\left( 5070-x \right)}{100}=699.50\]