The cost price of 9 articles is the selling price of 11 articles

Q.

Question 110 (i)

A store is having a 25% discount sale. Sheela has a Rs.50 gift voucher and wants to use it to buy a board game marked for Rs.320. She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable. Method 1 Subtract Rs.50 from the price and take 25% off the resulting price. Method 2 Take 25% off the original price and then subtract Rs.50.
Do you think both the methods will give the same result? If not, predict which method will be beneficial for her.

Solution

Given that the CP of 10 articles is equal to the SP of 9 articles.

Let the CP of 1 article =Rs. 1

Then the CP of 10 articles =1×10=Rs.10

Since, given that

SP of 9 articles = CP of 10 articles

SP of 9 articles =Rs.10

Now we calculate the CP of 9 articles.

CP of 9 articles =1×9=Rs.9

Thus,

Profit made on the selling of 9 articles = SP of 9 articles − CP of 9 articles

Profit made on the selling of 9 articles =Rs. 10−9=Rs.1

Profit or, Gain % =ProfitCost Price×100%

Gain %=19×100%

Gain %=11.11%

Answer

Verified

Hint: We will assume the selling price of 9 articles as x so we will also get the cost price of 10 articles as x, and then we will find the selling price of 1 article and also the cost price of 1 article. We will then find the profit as profit = SP - CP. Using these values we will find the profit percentage, which is given by $gain\%=\dfrac{gain}{C.P}\times 100$ .

Complete step by step answer:
Let us take the selling price (S.P.) of 9 articles to be Rs. x.
Now, from this we can say that the S.P. of 1 article is
\[=Rs.\ \dfrac{x}{9}\]
Now, as given in the question, we know that the cost price(C.P.) of 10 articles is also Rs. x.
So, from this, we can get the C.P. of 1 article is
\[=Rs.\ \dfrac{x}{10}\]
Now, the profit made by selling 9 articles can be calculated as follows
Profit=selling price of 9 articles -cost price of 9 articles
 Profit=x-9 times the cost price of 1 articles
(As assumed at the start of the question)
\[\begin{align}
  & =x-9\times \dfrac{x}{10} \\
 & =\dfrac{x}{10} \\
 & =\dfrac{x}{10} \\
\end{align}\]
Hence, this is the profit that is experienced.
Now, for the profit percent, we can use the formula that is as follows,
\[\begin{align}
  & \Rightarrow profit\%=\dfrac{profit}{C.P.}\times 100 \\
 & \Rightarrow profit\%=\dfrac{\dfrac{x}{10}}{9\times \dfrac{x}{10}}\times 100 \\
 & \Rightarrow profit\%=\dfrac{1}{9}\times 100\% \\
 & \Rightarrow profit\%=11.11\% \\
\end{align}\]

Hence we get the profit percentage = 11.11%

Note: Another method of doing this question is that we could simply take the cost price of 1 article to be Re. 1.
Then, we can proceed further as directed in the question and then we can use the formula for finding the profit % to get the final answer which would be the same as this one. Also, some students may make mistakes while writing the formula of profit percentage and may write SP instead of CP in the formula, so this must be avoided.