Question

A dealer originally bought 100 identical batteries at a total cost of \[q\] dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of \[q\], for how many dollars was each battery sold?
A) \[\dfrac{{3q}}{{200}}\]
B) \[\dfrac{{3q}}{2}\]
C) \[150q\]
D) \[\dfrac{q}{{100}} + 50\]
E) \[\dfrac{{150}}{q}\]

Answer 1

Hint:
Here, we will divide the total cost by 100 and then we will find the selling price by adding the above battery cost price with the \[50\% \] of each cost price. Then we will simplify the expression to find the required value.

Complete step by step solution:
We are given that a dealer originally bought 100 identical batteries at a total cost of \[q\] dollars.
Therefore, each battery cost price is Rs \[\dfrac{q}{{100}}\].
Then according to the question, we will find the selling price by adding the above battery cost price with the \[50\% \] of each cost price, we get
\[ \Rightarrow \dfrac{q}{{100}} + 50\% \times \dfrac{q}{{100}}\]
Using the percentage value in the above equation, we get
\[
   \Rightarrow \dfrac{q}{{100}} + \dfrac{{50}}{{100}} \times \dfrac{q}{{100}} \\
   \Rightarrow \dfrac{q}{{100}} + \dfrac{q}{{200}} \\
 \]
Taking common denominator in the above equation, we get
\[
   \Rightarrow \dfrac{{2q + q}}{{200}} \\
   \Rightarrow \dfrac{{3q}}{{200}} \\
 \]
Thus, the selling price of each identical battery would be \[\dfrac{{3q}}{{200}}\].

Hence, option A is correct.

Note:
We need to know that while solving these types of the question when we are given the cost price of many items, then we have to divide that many items with the total cost to find each cost price.