Price

[Guest]

A shopkeeper purchased one shoe rack, one cupboard and one table.

The cost price of the cupboard was twice that of the shoe rack and the
cost price of the table was \$6000 less than that of the cupboard.

He sold the shoe rack at 20% profit, the cupboard at 10% loss
and the selling price of the table was \$5760 more than the
selling price of the shoe rack.

He earned a total profit of 4%.

What was the cost price of one shoe rack ?


Let R = Rack

C = Cupboard

T = Table

C = 2R

T = C - 6000

T = R + 5760


I am stuck at this point.

[Guest]

Cost equations.....
C = 2R
T = C - 6000

Selling equations.....

1.2R + 0.99C + 5760 + 1.2R = 1.04(C + T + R)
1.2R + 0.99x2R +5760 + 1.2R = 1.04(2R + 2R-6000 + R)
5760 + 6240 = 5.2R - 4.38R
12000 = 0.82R
R = 14634.15

[Guest]

" 1.2R + 0.99C + 5760 + 1.2R = 1.04(C + T + R)
1.2R + 0.99x2R +5760 + 1.2R = 1.04(2R + 2R-6000 + R) "

I am not clear on these steps.

[Guest]

I think there is another typo error here....????.....why did you not try it yourself..????

20% profit for Rack is 1.2R......
10% loss for Cupboard is 0.90C
Table sold for (5760 + 1.2R)
Add them all up and that should be (1.04 x total cost) .... 4% more than the cost price because 4% total profit

1.2R + 0.90C + 5760 + 1.2R = 1.04(C + T + R)
1.2R + 0.90x2R +5760 + 1.2R = 1.04(2R + 2R-6000 + R) "
5760 + 6240 = 5.2 - 4.2R
12000 = R

[Guest]

5760 + 6240 = 5.2 - 4.2R
12000 = R

Still a typo error here..... should be....

5760 + 6240 = 5.2R - 4.2R
12000 = R

[Guest]

" why did you not try it yourself..???? "

I did not understand what the 1.2R and 1.04 was.

" 1.2R + 0.90C + 5760 + 1.2R = 1.04(C + T + R) " I did not know the reasoning why the first part equals the second.

[Guest]

Please reply. Thanks.

[Guest]

" why did you not try it yourself..???? "

I did not understand what the 1.2R and 1.04 was.

" 1.2R + 0.90C + 5760 + 1.2R = 1.04(C + T + R) " I did not know the reasoning why the first part equals the second.

I thought you meant "you did not understand it" but understood after my last post......

This is my previous post again.......

20% profit for Rack is 1.2R......
10% loss for Cupboard is 0.90C
Table sold for (5760 + 1.2R)
Add them all up and that should be (1.04 x total cost) .... 4% more than the cost price because 4% total profit

1.2R + 0.90C + 5760 + 1.2R = 1.04(C + T + R)
1.2R + 0.90x2R +5760 + 1.2R = 1.04(2R + 2R-6000 + R) "
5760 + 6240 = 5.2R - 4.2R
12000 = R

The Rack was sold at 20% profit. That means 20% more than it cost.
If it cost R to buy, then it was sold for (R + 20% of R). 20% is 20/100 = 0.2 so that same as ( 1xR + 0.2xR) = 1.2xR OR 1.2R.
The same reasoning for the cupboard but that is loss of 10% so sold for 0.90xC = 0.90C

The total cost to buy was ( C + T + R )
But from the buying equations this is same as ( 2R + 2R-6000 + R )......and this is total buying cost price
The total selling price was 4% more.....4% is 4/100 = 0.04........so selling price is 1.04 x buying cost price
So that becomes........ 1.04(2R + 2R-6000 + R)

[Guest]

" I thought you meant "you did not understand it" but understood after my last post...... "

I did not understand the 1.2r, the 1.04 , the first 2 steps of the solution, and why the first part equals the second.

I understand now.

Thanks again.

[Guest]

I have a related follow-up question:

Is the R also considered as 1 due to other problems having a variable representing the unknown ?

[Guest]

Is the R also considered as 1 due to other problems having a variable representing the unknown ?

I do not understand your question....?????


R is the buying or cost price for the shoe Rack.....

The same as........

C is the buying or cost price for the Cupboard.....

The same as.......

T is the buying ot cost price for the Table......

[Guest]

I'll reword the question:

Since the problem asks for the cost of the rack R, can R be considered as 1 also due to being an unknown value ?

Example: Let x = whatever value. Is that also considered as 1 ?

[Guest]

R does not represent any item of equipment bought or sold, it represents the value or the amount of money paid to buy the shoe Rack...the cost price.
and similar for the Cupboard and Table.......

This is your original post showing what you let each variable equal.

Let R = Rack .............the cost to buy the Rack

C = Cupboard ...........the cost to buy the Cupboard

T = Table ...............the cost to buy the Table

C = 2R .....................the Cupboard cost twice as much as the Rack

T = C - 6000 .....................the Table cost 6000 less than the Cupboard

We then followed what happened when they were sold as shown in the selling equations
and this was 4% more that the total cost (C + T + R)
We then wrote the whole equation in terms of R only and solved for R
and found R = 12000.
So the cost price to buy the shoe Rack is 12000 dollars
There was only 1 shoe Rack bought but the value or R, its cost price was 12000 dollars
Same for the Table and Cupboard,,,,there was only 1 of each of these bought as well.

[Guest]

Ok, I see what you mean. Thanks again.