Sales tax

S

Saumyojit

Senior Member
Joined
Jan 21, 2020
Messages
1,032
A storekeeper sold a wrist watch for $660, including a sales tax of 10%.If the cost price of the watch is $500, what is the percentage profit for shopkeeper?

My approach is that: if 10 percent is included in rs 660 then sales tax is 10 percent of 660 =66rs

Then sp is 594 then profit is rs 94.




where am i wrong?
 
Saumyojit said:
A storekeeper sold a wrist watch for $660, including a sales tax of 10%.If the cost price of the watch is $500, what is the percentage profit for shopkeeper?

My approach is that: if 10 percent is included in rs 660 then sales tax is 10 percent of 660 =66rs

Then sp is 594 then profit is rs 94.

where am i wrong?
Click to expand...
How is sales tax calculated in your country?

Typically, you take 10 percent of the before-tax cost. But you have taken is as 10 percent of the cost including tax! Does that make any sense?

If the before-tax price was 594, then the tax would be 0.10*594 = 59.4, and the total price would be 653.4, not 660.

Instead, you should use algebra. If the before-tax cost is x, then the tax is 10% of x. Write an equation that says the price including tax is 660, and solve. That will tell you how much the shopkeeper gets.

There are undoubtedly formulas that let you do this without algebra, but we've seen the danger of solving problems using formulas without thinking, so I wouldn't recommend it.
 
Dr.Peterson said:
How is sales tax calculated in your country?

Typically, you take 10 percent of the before-tax cost. But you have taken is as 10 percent of the cost including tax! Does that make any sense?

If the before-tax price was 594, then the tax would be 0.10*594 = 59.4, and the total price would be 653.4, not 660.

Instead, you should use algebra. If the before-tax cost is x, then the tax is 10% of x. Write an equation that says the price including tax is 660, and solve. That will tell you how much the shopkeeper gets.

There are undoubtedly formulas that let you do this without algebra, but we've seen the danger of solving problems using formulas without thinking, so I wouldn't recommend it.
Click to expand...

Suppose there is a statement there is a class of 200 students including 20 percent girls .
then the no of girls will be 20/100 * 200=....
 
In this case, the base of the percentage is the entire class: 20% of the entire class are girls.

That is entirely different from the sales tax case.

(Unless, in some places, tax could be calculated as a percentage of the total take, which is why I asked how it is calculated in your country. That's also why I prefer not to answer finance questions: definitions depend not on math but on law or customs that I might not know.)

In percent problems, it is always essential first to determine the base before you do anything else.
 
if i say 20 percent then base means 100 ? 20/100 means out of 100 or out of which total qunatity i am taking 20 percent?
 
The base is the number that something is a percent of; so it's the number you divide by. It can also be called the "whole" of which some quantity is a "part".

As I said,

In this case, the base of the percentage is the entire class: 20% of the entire class are girls.​

So if there are 53 girls in a class of 242, the percent of girls is 53/252 = 0.219; as a percentage, this is 21.9/100, or 21.9%. To convert the decimal to a percentage, you multiply by 100% (which is another way to say 1): 0.219 * 100% = 21.9%.

Here, the base was 242; that was the number I divided by.
 
out of 100 is 10 sales tax
then out of 1 will be : 10/100
then out of 660 will be : 10/100 * 660= 66 rs

wrong still ??
 
In the US, sales tax is usually computed as a percentage of the list price.

So if price plus tax is 660 and tax is 10%, then

[MATH]p + 0.1p = 660 \implies p(1 + 0.1) = 660 \implies 1.1p = 660 \implies p = \dfrac{660}{1.1} = 600.[/MATH]
In other words, the shop keeper will charge 660 but keep only 600.

So the profit is??????
 
JeffM said:
In the US, sales tax is usually computed as a percentage of the list price.

So if price plus tax is 660 and tax is 10%, then

[MATH]p + 0.1p = 660 \implies p(1 + 0.1) = 660 \implies 1.1p = 660 \implies p = \dfrac{660}{1.1} = 600.[/MATH]
In other words, the shop keeper will charge 660 but keep only 600.

So the profit is??????
Click to expand...
yes i know the solution but how my approach is wrong :


out of 100 is 10 sales tax
then out of 1 will be : 10/100
then out of 660 will be : 10/100 * 660= 66 rs

wrong still ??
660 is the base i have taken
 
Because the sales tax is included in the 660 so that tax was NOT calculated based on the 660. Sales tax is calculated on the list price, not the list price plus tax
 
You need to realize that if you take 10% of different numbers you get different answers!

There is some price for an item. Then on that price 10% is added on. Now you have the total price.

Now to go backward--to find the price for an item. If you subtract 10% of the toal price to find the original price you are subtracting too much sales tax. The sales tax is on the original price not the total price.
 
HOw ami subtracting too much sales tax ? x amt of sales tax money is in 660 rs.
10 percent is quantity
10/100 * 660 =66 rs is sales tax
remaing is the original sp (c.p+ profit)
 
Do a quick exercise:

1) Start with 100,
2) Subtract 10% of that number.
3) Write down your result.
4) Add 10% of this second number.
5) Show that final result.
 
Saumyojit said:
HOw ami subtracting too much sales tax ? x amt of sales tax money is in 660 rs.
10 percent is quantity
10/100 * 660 =66 rs is sales tax
remaing is the original sp (c.p+ profit)
Click to expand...
First you must do what tkhunny suggested in his post.

The sale tax is computed from the original price, which is NOT 660. The 660 amount came from adding on the sale tax to the original price which is less than 660!!! Again, if you take 10% of different numbers you will get different answers.
 
tkhunny said:
Do a quick exercise:

1) Start with 100,
2) Subtract 10% of that number.
3) Write down your result.
4) Add 10% of this second number.
5) Show that final result.
Click to expand...


99 coming but what does that prove?


10 percent is included in rs 660 then sales tax is 10 percent of 660 =66rs

Then sp is 594

here i am doing one time subtraction and Then sp is 594 . I am not adding 10 percent on rs 594 again.!
 
Saumyojit said:
99 coming but what does that prove?


10 percent is included in rs 660 then sales tax is 10 percent of 660 =66rs

Then sp is 594

here i am doing one time subtraction and Then sp is 594 . I am not adding 10 percent on rs 594 again.!
Click to expand...
But if you did add 10% to 594 you will NOT get back to 660.
You are saying that the original price of the item plus 10% sales tax will be 660. But this does NOT work out if you use 594 for the original price. PLEASE try it for yourself!
 
but if i go according to the question from backwards it clearly says 10 percent is included in 660 so if i need to exclude sales tax i need to subtract 10 percent from 660 which gives me rs 594.
 
Let's try this:

Suppose I tell you that I have a secret number. When I increase that number by 10%, the result is 550. You want to find my number.

Following your method, you would subtract 10% of 550, which is 55, and tell me that my number was 550 - 55 = 495.

But if you check that, you find that 495, increased by 10%, is 495 + 49.5 = 544.5, so that can't be my secret number!

Instead, you can recognize that by adding 10% to my number, I am adding 100% and 10%, so that the result is 110% of my number, that is, 1.1 times my number. Then you can find my number by undoing that multiplication: 550/1.1 = 500.

And that checks out: If you increase 500 by 10%, you get 500 + 50 = 550.

Do you see that this way works, and the other doesn't?

The reason is that the 10% that was added is not 10% of the 550 I got after the increase, but 10% of the original number, 500. So subtracting 55 was wrong.

In the sales tax case, similarly, the 10% tax is 10% of the before-tax amount, not 10% of the 660. Your method subtracts too much.
 
Dr.Peterson said:
Let's try this:

Suppose I tell you that I have a secret number. When I increase that number by 10%, the result is 550. You want to find my number.

Following your method, you would subtract 10% of 550, which is 55, and tell me that my number was 550 - 55 = 495.

But if you check that, you find that 495, increased by 10%, is 495 + 49.5 = 544.5, so that can't be my secret number!

Instead, you can recognize that by adding 10% to my number, I am adding 100% and 10%, so that the result is 110% of my number, that is, 1.1 times my number. Then you can find my number by undoing that multiplication: 550/1.1 = 500.

And that checks out: If you increase 500 by 10%, you get 500 + 50 = 550.

Do you see that this way works, and the other doesn't?

The reason is that the 10% that was added is not 10% of the 550 I got after the increase, but 10% of the original number, 500. So subtracting 55 was wrong.

In the sales tax case, similarly, the 10% tax is 10% of the before-tax amount, not 10% of the 660. Your method subtracts too much.
Click to expand...
YEs thats because in the question it says A storekeeper sold a wrist watch for $660, including a sales tax of 10%.
its says including .

Rather if it was said that A storekeeper sold a wrist watch for $660, giving a sales tax of 10%. on orignal sp OR by increasing 10 percent of orignal sp, then i would be obvious

that i need to add x + 10x/100 =660
 
You must log in or register to reply here.
Top