Find the percentage loss in the purchase and sale of bananas

[chwala]

Homework Statement

The cost price of $10$ bananas is equal to the selling price of $12$ bananas. Find the percentage loss.

Relevant Equations

Buying price and selling price

Ok my approach on this, i let the cost price = $x$, then it follows that cost price per banana will be given by;

$\frac {x}{10}$=$\frac {x}{12}$
$\frac {x}{10}-\frac {x}{12}$= loss
$x$$\left[ \frac {1}{10}-\frac {1}{12}\right]$=loss
$x$$\left[ \frac {1}{6}\right]$=loss
therefore the percentage loss is $\frac {1}{6}$×$100$= $16.666666$%

note;
i do not have the solution...and my working steps may not be correct...

 

[Mark44]

Homework Statement:: The cost price of $10$ bananas is equal to the selling price of $12$ bananas.
Find the percentage loss.
Relevant Equations:: Buying price and selling price

Ok my approach on this, i let the cost price = $x$, then it follows that cost price per banana will be given by;

$\frac {x}{10}$=$\frac {x}{12}$

This equation makes no sense. The only solution is x = 0.

$\frac {x}{10}-\frac {x}{12}$= loss
$x$$\left[ \frac {1}{10}-\frac {1}{12}\right]$=loss
$x$$\left[ \frac {1}{6}\right]$=loss
therefore the percentage loss is $\frac {1}{6}$×$100$= $16.666666$%

note;
i do not have the solution...and my working steps may not be correct...

 

[anuttarasammyak]

I am not good at economics at all and assumed that gain ratio is $\frac{s-c}{s}=1-\frac{c}{s}$ where c is cost or buying price and s is selling price. It would become loss ratio with minus sign when it is negative, e.g. -25% gain equals 25% loss.

 

[chwala]

This equation makes no sense. The only solution is x = 0.

Mark hi, true the very first equation $\left[ \frac {x}{10}=\frac {x}{12}\right]$ does not make sense.

On follow up (my thinking is based on) let us let the cost price be $x=40$=selling price,... then loss will be given by; the equation,
$\left[ \frac {40}{10}-\frac {40}{12}\right]$=loss per banana. From this i should get the loss percentage directly as indicated in post $1$. The problem i have probably is on the required form of the equation.

 

[PeroK]

I am not good at economics at all and assumed that gain ratio is $\frac{s-c}{s}=1-\frac{c}{s}$ where c is cost or buying price and s is selling price. It would become loss ratio with minus sign when it is negative, e.g. -25% gain equals 25% loss.

Profit and loss are normally measured against the initial capital, not the income. For example, if you start with $100 and end up with $75, then that is a 25% loss, not a 33.3% loss.

Certainly if you lost all your money that would be 100% loss and not an undefined loss!

 

[anuttarasammyak]

Thanks. I am poor at literacy of these kinds. In more physical sense output/input is $\frac{s}{c}$. Say it is 75%, loss is 25%. I hope I am on a right way.

 

[sysprog]

"The cost price of 10 bananas is equal to the selling price of 12 bananas."

Doesn't that mean that you're selling at 10/12 (5/6) of your buying price, and buying at 12/10 (120%) of your selling price? $-$ if so, then you're paying 12 and getting 10, so out of every 12 you're putting in, you're losing 2, and 12 divided by 2 is 6, so you're losing 1/6 (16(recurring 6)%), right?

 

[mjc123]

Your answer is correct, but your working is not - or at least, you're missing out some steps, which makes it unclear. You write:

x[1/10−1/12]=loss
x[1/6]=loss

Now 1/10 - 1/12 = 1/60, and the loss per banana is x/60. But since the cost per banana is x/10, the fractional loss is (x/60)/(x/10) = 1/6.

 

[chwala]

Your answer is correct, but your working is not - or at least, you're missing out some steps, which makes it unclear. You write:

Now 1/10 - 1/12 = 1/60, and the loss per banana is x/60. But since the cost per banana is x/10, the fractional loss is (x/60)/(x/10) = 1/6.

Just check your subtraction again...I see a mistake in your working.
True, my steps are not entirely correct...

 

[mjc123]

1/10 - 1/12 = 6/60 - 5/60 = 1/60. Confirm with a calculator.

 

[chwala]

1/10 - 1/12 = 6/60 - 5/60 = 1/60. Confirm with a calculator.

True, i missed that...

 

[chwala]

Your answer is correct, but your working is not - or at least, you're missing out some steps, which makes it unclear. You write:

Now 1/10 - 1/12 = 1/60, and the loss per banana is x/60. But since the cost per banana is x/10, the fractional loss is (x/60)/(x/10) = 1/6.

...that makes sense...i.e in business math we know that;
Loss/Profit=$\left[\frac {cost price- sale price}{cost price}\right]$...then percentage loss or profit would follow by,
Percentage Loss/Profit=$\left[\frac {cost price- sale price}{cost price}\right]×100$.