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 the list price of the chair.
Answers
Answer:
A shopkeeper sells a table at 8% profit and a chair for 10% disc. He gets Rs1008. If he sells table for 10% profit and 8% discount he would have Rs 20 more. Find the CP of table and MP of chair.
Case (1):
Table is sold at a profit of 8%
= SP of table = x + 8x/100 = 108x/100
Chair is sold at a discount of 10%
= SP of chair = y - 10y/100 = 9y/10
Given that table and chair are sold for Rs 1008,
(108x/100) + (9y/10) = 1008
= 108x + (90y/100) = 1008
= 108x + 90y = 100800
= 6x + 5y = 5600
= x = (5600 - 5y) / 6 -------------------------- (i)
Case (2):
Table is sold at a profit of 10%
SP of table = x + 10x/00 = 11x/10
Chair is sold at a discount of 8%
= SP of chair = y - 8y/100 = 92y/100
Given that table and chair are sold for Rs 1028
11x/10 + 92y/100 = 1028
= 110x + 92y/100 = 1028
= 110x + 92y = 102800
Substituting the value of (i)
110 [(5600 - 5y)/6] + 92y = 102800
= (616000 - 550y)/6 + 92y = 102800
= (616000 - 550y + 552y)/6 = 102800
= (616000 + 2y)/6 = 102800
= 616000 + 2y = 616800
= 2y = 800
= y = Rs 400
From (i),
x = (5600 – 5 × 400)/6
x = (5600 - 2000)/6
x = 3600/6
= x = Rs 600
Therefore, CP of table = Rs 600
Marked price of chair = Rs 400
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