# A dealer declares to sell his goods at cost price, but he uses a false weight and gains $6\dfrac{{18}}{{47}}\% $ for a kilogram, he uses a weight of:

\[(A)\]. $947g$

\[(B)\]. $960g$

\[(C)\]. $940g$

\[(D)\]. $947g$

Last updated date: 19th Mar 2023

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Answer

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Hint: Use gain percentage formula

Let the incorrect weight (IW) be $x$ kg.

The correct weight (CW) is 1 kilogram. As the dealer sells goods at cost price yet he makes profit. The profit he makes is due to false or incorrect weight he uses when he sells his goods. In this case we have to find the false weight he uses to make profit.

Now,

$ \Rightarrow $gain$\% $=\[\left( {\dfrac{{CW - IW}}{{CW}}} \right)\]x\[100\]

Where \[CW = 1,IW = x\],then

Applying the formula, we get

$ \Rightarrow $\[gain\% = \left( {\dfrac{{1 - x}}{1}} \right)\]x100

$ \Rightarrow $\[6\dfrac{{18}}{{47}} = \left( {\dfrac{{1 - x}}{1}} \right)\]x100

$ \Rightarrow $\[\dfrac{{300}}{{47}} = \left( {\dfrac{{1 - x}}{1}} \right)\]x100

Solving the above equation by cross multiplying

$ \Rightarrow $\[300(1) = 47(1 - x)\]x100

$ \Rightarrow $\[3 = 47 - 47x\]

$ \Rightarrow $\[47x = 44\]

$ \Rightarrow $\[x = \dfrac{{44}}{{47}}\]kg

$ \Rightarrow $\[x = 940g\]

So, the incorrect weight (IW) =\[940g\]

So, option (C) is correct.

Note: Whenever we came up with this type of problem then the easiest and efficient way to solve the problem is using the formula. By applying formulas directly such questions can be easily solved and we get correct solutions in less time. Only we have to understand what the question is saying. If we understand that then we can know which formula we have to apply.

Let the incorrect weight (IW) be $x$ kg.

The correct weight (CW) is 1 kilogram. As the dealer sells goods at cost price yet he makes profit. The profit he makes is due to false or incorrect weight he uses when he sells his goods. In this case we have to find the false weight he uses to make profit.

Now,

$ \Rightarrow $gain$\% $=\[\left( {\dfrac{{CW - IW}}{{CW}}} \right)\]x\[100\]

Where \[CW = 1,IW = x\],then

Applying the formula, we get

$ \Rightarrow $\[gain\% = \left( {\dfrac{{1 - x}}{1}} \right)\]x100

$ \Rightarrow $\[6\dfrac{{18}}{{47}} = \left( {\dfrac{{1 - x}}{1}} \right)\]x100

$ \Rightarrow $\[\dfrac{{300}}{{47}} = \left( {\dfrac{{1 - x}}{1}} \right)\]x100

Solving the above equation by cross multiplying

$ \Rightarrow $\[300(1) = 47(1 - x)\]x100

$ \Rightarrow $\[3 = 47 - 47x\]

$ \Rightarrow $\[47x = 44\]

$ \Rightarrow $\[x = \dfrac{{44}}{{47}}\]kg

$ \Rightarrow $\[x = 940g\]

So, the incorrect weight (IW) =\[940g\]

So, option (C) is correct.

Note: Whenever we came up with this type of problem then the easiest and efficient way to solve the problem is using the formula. By applying formulas directly such questions can be easily solved and we get correct solutions in less time. Only we have to understand what the question is saying. If we understand that then we can know which formula we have to apply.

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