Question

A shopkeeper sells a table at 8% profit and a chair at 10% discount thereby getting 1008. If he had sold the table at 10% profit and chair at 8% discount he would have got 20 more. Find the cost price of the table and list price of the chair.​

Answer 1

Answer:

Step-by-step explanation:

Given,

Profit on table =8%

Discount on chair =10%

Let  

C.P. of table = Rs x and  

C.P. of chair = Rs y

Then according to the question,

100

x×(100+8)

​  

+  

100

y×(100−10)

​  

=1008

⇒108x+90y=100800

⇒6x+5y=5600      … (i)

And,

100

x×(100+10)

​  

+  

100

y×(100−8)

​  

=1008+20

⇒110x+92y=102800

⇒55x+46y=51400      … (ii)

Now, multiplying (i) by 55 and (ii) by 6, we have

330x+275y=308000       ... (iii)

330x+276y=308400       ... (iv)

Subtracting equation (iv) from (iii), we get

−y=−400

⇒y=400

On substituting the value of y in equation (i), we get

6x+5(400)=5600

⇒6x=5600−2000

⇒x=  

6

3600

​  

 

⇒x=600

Hence,  

Cost Price of the table = Rs 600

List price of chair =400×  

100

90

​  

= Rs 360

Answer 2

Answer:

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GIVEN

☄️case1

profit on table = 8%

discount on chair= 10%

money he received= Rs. 1008

☄️case 2

profit on table= 10%

discount on chair= 8%

money he received= 1008 + 20= Rs. 1028

To find

cost price of the table and the list price of the chair.

Solution

let the cost price of the table be Rs. X and ,

the cost price of the chair be Rs y.

According to the question:

$\bold{ \frac{x \times (100 + 8)}{100} + \frac{y(100 - 10)}{100} = 1008 }$

By solving this further we get,

⇒ 108x + 90y= 108000

⇒6x + 5y= 5600 .....(i)

And,

$\bold{ \frac{x \times (100 + 10)}{100} + \frac{y(100 - 8)}{100} = 1008 + 20}$

⇒ 110x + 92y = 102800

⇒ 55x + 46 y= 51400. ....(ii)

By solving equation (i) and (ii) with elimination method we get

⇒ y = 400

Now by substituting the value of y in equation (i) we get,

6x + 5 x 400 = 5600

⇒ 6x = 5600- 2000

⇒ x= 3600/6

⇒ x= 600

Hence,

Hence, Cost Price of the table = Rs 600

List price of the chair=

$\bold {400 \times \frac{90}{100} = Rs360}$