Question

A glassware seller bought 1000 glass tumblers. 100 of them were broken and she sold the remaining tumbler at Rs 80 each. If she made a loss of 4%, at what proce did she purchase each tumbler?​

Answer 1

Answer:

$75

My answer might be a bit off since I'm not really sure what you mean by "Rs 80", which I interpreted as $80, but if my interpretation is wrong, you can still use all the same steps and you should get the correct answer

Step-by-step explanation:

So we can represent the price of each tumbler as the variable "P", since it's some unknown value we're solving for. Let's also just say that "T" is the total price that she paid for all of the tumblers.

Using this equation we can derive the following equation.

1000P = T

Since multiplying the price of each glass tumbler times the price of one glass tumbler should equal the entire price.

Now she only sold 900 of them, since 100 were broken, and she sold them each for 80. So knowing this we can find how much she made in total from selling the remaining 900 glass tumblers

900 * 80 = 72,000

Now if she made a loss of 4%, that means the total money she made back, is only 96% the amount of money she paid for the product. The reason for this is (100-4)% represents a 4% loss.

Remember, how T represents the entire price, well we know that 72,000 represents 96% of it's value. To find what x% is of some number, you generally convert the percentage into a decimal by dividing by 100, so to find x% of some variable "a" you generally use the following equation: $a*\frac{x}{100}$ where the value of this expression will be equal to x% of a.

So let's convert 96% to decimal form: $\frac{96}{100} = 0.96$. Now if we multiply this decimal 0.96 by T, we should get 72,000 since the 72,000 represents 96% of the original value

$0.96T = 72,000$

To find the original value of T, we simply divide both sides by 0.96

$T = 75,000$

So now that we know the original total price, we can use the original equation we derived to solve for P, which represents the price of each individual tumbler.

Original Equation

$1000P = T$

Substitute 75,000 as T

$1000P = 75,000$

Divide both sides by 1,000

$75=P$

This means she sold each for 75