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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 ?

Fin27
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  • Have you taken into account the loss he would be suffering at the time of buying i.e. he will buy less (800 g) than actual (1000 g) Can you please write an answer as per your reasoning – Fin27 Mar 22 '23 at 08:42
  • Oh ok so instead of buying 800 grams, he is actually getting a benefit of 1000 g. Please feel free to post an answer as per your convenience , the equation for this particular variation in which there is a use of faulty weight at the the time of buying is getting turning out to be challenging – Fin27 Mar 23 '23 at 22:13

1 Answers1

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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 $800$.

D S
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  • While buying from dealer, why will he pay $1000CP$ and not $800CP$ . I mean if his balance is faulty shouldn't the shopkeeper's balance read 800 gram when in fact he is buying 1000 grams from the dealer ? Can we then reach to author's equation ? – Fin27 Mar 25 '23 at 18:31
  • no, his balance shows $1000$g when he buys $800$g in reality – D S Mar 25 '23 at 18:35
  • Imagine when the dealer arrives at the shopkeeper's place and put 1 kg amount of something on his balance, Since it measures 200 gram less, it should read 800 grams, so why will shopkeeper give dealer $1000*CP$, when he can clearly witness that the goods are instead weighing 800 gram ?

    Measures 800 gram is the weight actually being measured right ?

    A bit confusing

     – Fin27 Mar 25 '23 at 18:59
  • "1 kg weight actually measures 800 gram". This means that the weight stone (or what do we call it?) has a label $1000$g. But it's weight is $800$g only. The shopkeeper uses this to measure the goods. The balance will be balanced for $800$g of goods, but the stone will read $1000$g. So, he has to pay $1000CP$. – D S Mar 25 '23 at 19:03
  • Ohh the weight is faulty, I started thinking on the faultiness of the weighing machine itself . Ok but still at the time of transaction, when this fake weight stone of 800 gram will be kept on one side of balance and the goods on the other side , if the goods actually weigh 1000 grams , then the balance won't actually be balanced, and till the time the there is no balance why will the transaction take place? how will 800 gram of fake weight balance off the 1000 g of actual goods ? – Fin27 Mar 25 '23 at 19:11
  • the goods have no tag on them mentioning how much grams they measure. Consider, for example, some tonnes of flour kept in a large can. How will the dealer keep exactly 1000g on one side? He keeps such an amount so that the beam is balanced. – D S Mar 25 '23 at 19:15
  • Ohhhh yes yes understood ! Thank you so much :) ,correct this question became a no-brainer . . . . Please have a look into this one :- https://math.stackexchange.com/questions/4666320/dishonest-shopkeeper-at-the-time-of-buying-as-well-as-selling .... This question actually has dishonesty on both buying as well as selling side – Fin27 Mar 25 '23 at 20:03