Is profit/loss% always wrt price

[rajeshmarndi]

A merchant professes to lose 4% on tea but uses a weight equal to 840 gm instead of 1 kg. Find his real loss% or profit%.

Book solution:
If cp(cost price) of 1 kg is x , then sp(selling price) of 1 kg = 96/100 x i.e .96x (4% loss). Which is actually sp of 840 gm.

cp of 840 gm= x/1000*840=.84x

So, when cp =.84x, sp is .96x
when cp=100 , sp = .96x/.84x*100=114.28

i.e 14.28% profit

My workout:
I want to solve it without using the price, like in the above. I know the merchant professes a loss of 4%.

i.e instead of giving 100gm tea, he is giving the customer 104 gm tea, i.e a loss of 4 gm tea.

Since he uses 840 gm in place of 1 kg. So when he will sell 1 kg tea, he professes a loss of 4% i.e he will give customer 1040 gm tea, which actally will be 840/1000*1040 = 873.6 gm.

So he is making a profit of 1000 - 873.6 = 126.4 gm on 1000gm.
So on 100 gm, his profit = 12.64%.

Whats wrong on my workout. is it that the loss/profit % is always on price?

Thank you.

 

[SteamKing]

A merchant professes to lose 4% on tea but uses a weight equal to 840 gm instead of 1 kg. Find his real loss% or profit%.

Book solution:
If cp(cost price) of 1 kg is x , then sp(selling price) of 1 kg = 96/100 x i.e .96x (4% loss). Which is actually sp of 840 gm.

cp of 840 gm= x/1000*840=.84x

So, when cp =.84x, sp is .96x
when cp=100 , sp = .96x/.84x*100=114.28

i.e 14.28% profit

My workout:
I want to solve it without using the price, like in the above. I know the merchant professes a loss of 4%.

i.e instead of giving 100gm tea, he is giving the customer 104 gm tea, i.e a loss of 4 gm tea.

Since he uses 840 gm in place of 1 kg. So when he will sell 1 kg tea, he professes a loss of 4% i.e he will give customer 1040 gm tea, which actally will be 840/1000*1040 = 873.6 gm.

So he is making a profit of 1000 - 873.6 = 126.4 gm on 1000gm.
So on 100 gm, his profit = 12.64%.

Whats wrong on my workout. is it that the loss/profit % is always on price?

Thank you.

In this case, price is what you have to go on. You don't know anything else about the tea merchant's business, only what is given in the problem statement.

I don't think your solution is valid because it gets the particular circumstances of the merchant's deception backwards.

The merchant is not giving his customers extra tea at the same price, as occurs in your approach; he is shorting the customer on the amount of tea each has thought was being purchased.

Instead of a customer getting 1000 grams of tea in his order, the merchant actually furnishes only 840 grams. What do you think happens to the missing 160 grams? Does the merchant drink it himself? Or does he turn around and sell it to another customer? Remember, this is the same 160 grams of tea which another customer thought he had already purchased from the merchant and took home.

It's like the old joke: we lose money on every sale, but we make up for it in volume.