Question

The excise duty on a certain item has been reduced to Rs. 760 from Rs. 950. Find the reduction percent in the excise duty on that item.

Answer 1

Hint: To solve this question, we will, first of all, calculate the reduced cost of the item by subtracting the new cost from the old cost. Then we will calculate the reduction percentage by the formula.
\[\text{Reduction Percentage}=\dfrac{\text{Old Price - New Price}}{\text{Old Price}}\times 100\]

Complete step-by-step answer:
We are given that the excise duty of an item was Rs. 950.
\[\Rightarrow \text{Old Cost/ Price of Item}=Rs.950\]
Given that it is reduced to Rs. 760.
\[\Rightarrow \text{New Cost/ Price of Item}=Rs.760\]
We will calculate the reduced cost by subtracting the new cost from the old cost.
\[\text{Reduced Cost}=\text{ Old Cost }-\text{ New Cost}\]
Substituting the value of old cost as Rs. 950 and new cost as Rs. 760, we have,
\[\Rightarrow \text{Reduced Cost}=Rs.950-Rs.760\]
\[\Rightarrow \text{Reduced Cost}=Rs.190\]
Hence, we have obtained the reduced cost as Rs. 190.
Finally, we will calculate the reduction percentage by using the formula.
\[\text{Reduction Percentage}=\dfrac{\text{Old Price - New Price}}{\text{Old Price}}\times 100\]
\[\Rightarrow \text{Reduction Percentage}=\dfrac{\text{Reduced Cost}}{\text{Old Price}}\times 100\]
Substituting the values of reduced cost and old price, we get,
\[\Rightarrow \text{Reduction Percentage}=\dfrac{\text{Rs}\text{.190}}{\text{Rs}.950}\times 100\]
\[\Rightarrow \text{Reduction Percentage}=\dfrac{1900}{95}\]
\[\Rightarrow \text{Reduction Percentage}=20\%\]
Therefore, the reduction percentage is 20 %.

Note: There is a difference between the reduction percentage and increment percentage. The increment percentage is given by \[\dfrac{\text{New Price }-\text{ Old Price}}{\text{Old Price}}\times 100.\] It is used when the new price is greater than the old price and reduction is when the new price is less than the old price.