Dishonest shopkeeper at the time of buying as well as selling

Question

James is a dishonest shopkeeper, and at the time of selling and purchasing, weighs 20% less and 10% more per kilogram respectively. Find the percentage profit earned by treachery. (Assume he sells at cost price)

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My attempt at solution:-

Let $CP$ be the cost price per gram , At the time of purchasing $1000$ grams of goods , he is actually purchasing $1100$ grams from the dealer , so his total cost price would be $1000*CP$ but he has a quantity of $1100$ grams. [I am not sure if weighs 10% more means this only]

Now for these 1100 grams, the customer gives the shopkeeper $1100*SP$ , however the customer actually gets $1100*0.8$ grams = $880$ grams in return, so the cost of these $880$ grams would be $880*CP$, therefore, $1100*SP=880*CP$, which gives answer as a loss of 20%, and that is incorrect.

Please help out on where am I going wrong .

Answer 1

Answer edited to correct a mistake in my analysis.

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James is a dishonest shopkeeper, and at the time of selling and purchasing, weighs 20% less and 10% more per kilogram respectively. Find the percentage profit earned by treachery. (Assume he sells at cost price).

First, James buys $~B~$ and receives $~A = 110\%~$ of $~B.~$

So, the initial investment of James is $~B,~$ and James now has $~A = 1.1 \times B.~$

Now, assume that James sells all that he has.

So the customer pays for $~C~$ and only receives $~A,~$ where $~A = 80\%~$ of $~C.$

Therefore,

$$A = 0.8 \times C \implies \\ C = \dfrac{A}{0.8} = 1.25 \times A = 1.25 \times (1.1 \times B) = 1.375 \times B.$$

So, the customer pays for $~1.375 \times B.$

Therefore, James now receives $~1.375 \times B.$

Therefore, James has spent $~B~$ and received $~(1.375 \times B)~$ in return.

Therefore, James' net profit is $~(1.375 \times B) - B = (0.375 \times B).$

Therefore, James' percentage profit will be

$$100\% \times \frac{\text{Net Profit}}{\text{Initial Investment}}$$

$$= 100\% \times \frac{0.375 \times B}{B} $$

$$= 100\% \times (0.375) = 37.5\%.$$

Answer 2

This problem is a bit different from the others you have asked about, as you'll notice:

Your logic till "$880$ grams in return, so the cost of these $880$ grams would be $880*CP$" is fine. However, you really can't equate this with $1100SP$ because they are not equal. This is due to the wrong weights. You seem to have missed the fact that he claims to sell at cost, but due to a discrepancy in the weights, this is not the case. You have reversed this thing, first, you calculate the effective cost price and selling price due to the wrong weights, and then use the fact that James sells at cost. This should be the other way around.

James buys $1100$g from dealer at $1000CP$. So, he buys $1$g at $\frac{10}{11}CP$. So, he buys $880$g in $800CP$. Sells the same $880$g in $1100CP$ (since he sells at cost, and tells the customer he is selling him $1100$g.) Now you can get the required profit, $37.5\%$. Sorry for the confusion before.