Question

A household product is marked \[30\% \] above its cost price. The percentage discount allowed to gain \[17\% \] is?

Answer 1

Hint: We have to find the percentage discount allowed to gain \[17\% \] for a product which is marked \[30\% \] above its cost price. As we know, if the cost price of an object is \[a\] and if the price increases by \[b\% \] then the price of object becomes \[a \times \dfrac{{100 + b}}{{100}}\]. The selling price of an object is the sum of the cost price and the gain amount. Here, we will first consider the cost price of the product to be \[x\]. Using that we will calculate the marked price and selling price with a gain of \[17\% \]. Then we will subtract the both to find the discount and then we will convert it into a percentage which will give the required result.

Complete step by step solution:
We have to find the percentage discount allowed to gain \[17\% \] for a household product which is marked \[30\% \] above its cost price.
Let the cost price of the given product is \[x\].
Given, the marked price of the product is \[30\% \] above its cost price.
As we know, if \[b\] is the percentage of the marked price, then marked price is given by
Marked price of the given item \[ = \] \[\dfrac{{100 + b}}{{100}} \times {\text{cost price}}\]
Using this, we get
Marked price of the product \[ = \] \[\dfrac{{100 + 30}}{{100}} \times x\]
\[ = \dfrac{{130x}}{{100}}\]
Now, we require a gain of \[17\% \].
As we know, if \[c\] is the percentage of gain, then
Selling price of the item \[ = \] \[\dfrac{{100 + c}}{{100}} \times {\text{cost price}}\]
Using this, we get
Selling price of the product \[ = \] \[\dfrac{{100 + 17}}{{100}} \times x\]
\[ = \dfrac{{117x}}{{100}}\]
As we know, \[{\text{discount}} = {\text{marked price}} - {\text{selling price}}\]
Therefore, the discount amount of the product \[ = \dfrac{{130x}}{{100}} - \dfrac{{117x}}{{100}}\]
\[ = \dfrac{{13x}}{{100}}\]
Now we have to find the percentage of discount, for this we will use the formula
\[{\text{discount}}\% = \dfrac{{{\text{discount}}}}{{{\text{marked price}}}} \times 100\]
Therefore, we get the percentage of discount\[ = \dfrac{{\dfrac{{13x}}{{100}}}}{{\dfrac{{130x}}{{100}}}} \times 100\% \]
On solving we get percentage of discount\[ = \dfrac{{13x}}{{100}} \times \dfrac{{100}}{{130x}} \times 100\% \]
\[ = 10\% \]
Hence, the percentage discount offered to gain \[17\% \] profit is \[10\% \].
So, the correct answer is “ \[10\% \].”.

Note: We can also solve this question by another process.
Let’s consider, the cost price of the product is \[Rs.{\text{ }}100\]. The marked price of the product is \[30\% \] above its cost price.
So, marked price of the product will be \[Rs.\left( {{\text{ }}100 + 100 \times \dfrac{{30}}{{100}}} \right)\] i.e., \[Rs.{\text{ }}130\].
Now, we require a gain of \[17\% \].
So, the selling price of the item will be \[Rs.{\text{ }}\left( {100 + 100 \times \dfrac{{17}}{{100}}} \right)\] i.e., \[Rs.{\text{ }}117\].
So, the discount will be \[\left( {Rs.{\text{ }}130 - Rs.{\text{ }}117} \right)\] i.e., \[Rs.{\text{ }}13\].
Therefore, the percentage of discount will be \[\left( {\dfrac{{13}}{{130}} \times 100\% } \right)\].
On simplifying we get, the percentage of discount is \[10\% \].