Question

A dishonest salesman sells his goods at a profit of 20%
while also using a weighing machine that weighs the
good 20% less in weight than marked. What is his total
percent gain?​

Answer 1

$\huge\pmb{♡A᭄ɴsᴡᴇʀ࿐ :−}$

Let us assume that 1000 g of goods cost Rs. 100.

Since he makes a Profit of 20%, the Selling Price would be:

$\begin{gathered} \sf \begin{gathered}\implies Profit\: \% = \dfrac{(SP - CP)}{CP } \times 100\\\\\\\implies 20 = \dfrac{ SP - 100}{ 100} \times 100\\\\\\\implies 20 = SP - 100\\\\\\\implies SP = 100 + 20 = \boxed{ \bf{ Rs. 120}}\end{gathered} \end{gathered}$

⟹Profit%=

CP

(SP−CP)

×100

⟹20=

100

SP−100

×100

⟹20=SP−100

⟹SP=100+20=

Rs.120

Hence for 1000 grams of goods, he sells them for Rs. 120 by which he earns a profit of 20%.

Now, it is given that, he also uses a weighing machine which weighs the goods 20% less than the original weight.

Hence 1000 g of goods in his weighing machine would weigh:

$\begin{gathered} \sf\begin{gathered}\implies \text{Actual weight} = 1000 - \dfrac{20}{100} \times 1000\\\\\\\implies \text{Actual Weight} = 1000 - 200 = \boxed{ \bf{800 g}}\end{gathered} \end{gathered}$

Hence his machine would show the weight of 800 g to be equal to 1000 g.

Therefore, for 1000 g = Rs. 120, then for 800 g the actual selling price would be:

⟹SP for 800 g =

1000

800×120

⟹ SP for 800 g=

Rs.96

But, the shopkeeper is selling it for Rs. 120. Hence profit made here is:

\begin{gathered}\begin{gathered}\implies Profit\: \% = \dfrac{120 - 96}{96} \times 100\\\\\\\implies Profit\: \% = \dfrac{24}{96} \times 100\\\\\\\implies Profit\: \% = \dfrac{100}{4} \\\\\\\implies Profit\: \% = \boxed{ \bf{ 25\:\%}}\end{gathered} \end{gathered}

⟹Profit%=

96

120−96

$\begin{gathered}\begin{gathered}\implies \text{SP for 800 g } = \dfrac{800 \times 120}{1000}\\\\\\\implies \text{ SP for 800 g} = \boxed{ \bf{Rs.\:\:96}}\end{gathered} \end{gathered}$

×100

⟹Profit%=

96

24

×100

⟹Profit%=

4

100

⟹Profit%=

25%

\sf \: Therefore \: the \: net \: profit \:gained \: by \: the \: dishonest \: shopkeeper \: is \: 25%Thereforethenetprofitgainedbythedishonestshopkeeperis25

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