A coat was sold by a shopkeeper at a gain of 5%. If it had been sold for 1650 less, he would have had a 5% loss. Find CP

Let cp of the article = x at 5% gain sp of article = x + (5/100)x = 1.05x at 5% loss sp of article = x - (5/100)x = 0.95x given that 1.05x - 0.95x = 1650 0.1x = 1650 x = 1650/0.1 Cost price (x) = Rs. 16500

Answer Link

johanrusli johanrusli · Answer 2 · 2019-10-30T08:06:32+01:00

The cost price is 16500

Further explanation

Let's learn about the basic formula about Profit and Loss

[tex]\texttt{Profit = Selling Price - Cost Price}[/tex]

[tex]\texttt{Selling Price = Cost Price ( 100\% + Profit\% )}[/tex]

[tex]\texttt{Loss = Cost Price - Selling Price}[/tex]

[tex]\texttt{Selling Price = Cost Price ( 100\% - Loss\% )}[/tex]

Let us tackle the problem !

Given:

Gain Percentage = 5%

Loss Percentage = 5%

Difference of Sales Price = 1650

Unknown:

Cost Price = ?

Solution:

[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 100\% + \texttt{Gain Percentage} )[/tex]

[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 100\% + 5\% )[/tex]

[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 105\% )[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 100\% - \texttt{Loss Percentage} )[/tex]

[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 100\% - 5\% )[/tex]

[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 95\% )[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{Difference of Sales Price} = \texttt{Initial Sales Price} - \texttt{Final Sales Price}[/tex]

[tex]1650 = \texttt{Cost Price} \times ( 105\% ) - \texttt{Cost Price} \times ( 95\% )[/tex]

[tex]1650 = \texttt{Cost Price} \times ( 105\% - 95\% )[/tex]

[tex]1650 = \texttt{Cost Price} \times ( 10\% )[/tex]

[tex]\texttt{Cost Price} = 1650 \div ( 10\% )[/tex]

[tex]\texttt{Cost Price} = 16500[/tex]

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Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces