Question

A shopkeeper professes to sell the goods at cost price, but he uses a weight of 900 grams for a kilogram. Then his gain percent is
(a) $\dfrac{100}{9}%$
(b) $\dfrac{100}{8}%$
 (c) $\dfrac{100}{7}%$
 (d) $\dfrac{100}{6}%$

Answer 1

Hint: Firstly, we should know the formula which we are going to use to calculate profit as Profit(P)= Selling Price(S.P.)-Cost Price(C.P.) and profit percent as $P\%=\dfrac{P}{C.P}\times 100$. Then, we have to calculate the profit by substituting the value of SP and CP. Then, on getting profit, we will find the value of the profit percentage by substituting the value of profit and CP. This procedure will give us the desired result.

Complete step-by-step answer:
In this question, we are supposed to find the profit percentage of the shopkeeper for weighing 900 gram for a kilogram.
Before attempting the question, we should know Cost price is the price at which the shopkeeper has bought it and Selling Price is the price at which he is selling that item. The selling price is greater than the cost price if the shopkeeper is earning the profit.
So, we must know the following formula as:
Profit(P)= Selling Price(S.P.)-Cost Price(C.P.)
Now, another formula is used to get the profit(P)% is as:
$P\%=\dfrac{P}{C.P}\times 100$
Now, by using the condition mentioned in the question, we may proceed further.
So, the shopkeeper is falsely weighing 900 gram instead of a kilogram and earning profit(P) as:
$\begin{align}
  & P=1000-900 \\
 & \Rightarrow P=100 \\
\end{align}$
From the above calculation, we came to know that the shopkeeper is making a profit of Rs 100 by making a false weighing.
Then, we will find the profit percentage(P%) which is given as the ratio of the profit(p) to the cost price(C.P.) multiplied by 100 as:
$\begin{align}
  & P\%=\dfrac{100}{900}\times 100 \\
 & \Rightarrow P\%=\dfrac{100}{9}\% \\
\end{align}$
So, we came to know that the shopkeeper is making a profit with a profit percent of $\dfrac{100}{9}\%$.
Hence, option (a) is correct.

Note: The most common mistake that we make while solving this type of the question is interchanging the value of SP and CP. If we take CP as 100 then the profit percentage will become 10% which is a wrong answer. We should be very clear in taking the values of CP and SP for these type of the questions as both of them are having units as rupees and also we should be aware of the formulas to calculate profit as Profit(P)= Selling Price(S.P.)-Cost Price(C.P.) and profit percent as $P\%=\dfrac{P}{C.P}\times 100$.