The cost price of 10 bananas is equal to the s.p. of 12 bananas. find the loss per cent.

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...

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...

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.

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

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.

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.

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

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.

"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?

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

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.

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

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

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.