Question :- A shopkeeper claims he sells at 10% profit but his 1 kg weight actually measures 800 gram when selling and buying. Find his Profit/Loss %
Author's solution :- $800 * 1000 * SP$ = $(11/10) * 1000 * 800*CP$ where SP is the selling price per gram and CP is the cost price per gram
$SP/CP=11/10$ , giving 10% profit
My attempt on understanding the explanation:-
I can't figure out how to use the profit/loss incurred during buying, but here is my take at the rest of the equation :-
Price on the tag at which he sells to the customer is :- $1000*CP*(11/10)$
Since the total selling price is not getting changed it would be equal to the price at which he sells 800 grams which would be $800*SP$
so if I ignore the profit/loss being incurred at the time of buying goods from the seller, I get the following equation :-
$1000*CP*(11/10)$ = $800*SP$
Now how shall I incorporate the loss at the buying in the equation ?
Sorry, I hadn't read "when selling and buying", hence my wrong (now deleted) comments.
This becomes a no-brainer now. He buys $800$g at whatever cost but sells the $800$g at $10\%$ profit on the cost.
Let's get to the equation. $SP$ is the selling price per gram, and $CP$ is the cost price per gram. The shopkeeper buys $800$g from the dealer at $CP$, but gives him $1000CP$ (due to the wrong weights). He takes $1000CP \cdot (11/10)$ from you for those $800$g, while you pay him $1000SP$ (thinking that you're buying $1000$g). Equate these. Don't really know why the author multiplied both sides by $800$.