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

Find the CP of table and MP of chair.

A shopkeeper sells a table at 8% profit and a chair for 10% disc. He gets Rs1008. If he sells table for 10% profitand 8% disc he get 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

Answer 2

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

Let the cost price of saree be Rs. 'x' and the list price of sweater be Rs. y.

Therefore,

$\bold\green{Situation 1 -}$

By selling a saree at 8 % profit and a sweater at 10 % discount, the shopkeeper gets Rs. 1008

⇒ 108x/100 + 90y/100 = 1008

⇒ 27x/25 + 9y/10 = 1008/1

Taking L.C.M. of the denominators and then solving it, we get.

54x + 45y = 50400 _________(1)

$\bold\green{Situation 2 -}$

by selling a saree at 10 % profit and a sweater at 8 % discount, the shopkeeper gets Rs. 1028.

$\sf{ \frac{110x}{100} + \frac{92y}{100} = 1028 }$

$\sf{ \frac{11x}{10} + \frac{23y}{25} = 1028}$

Taking L.C.M. of the denominators and then solving it, we get.

⇒ 55x + 46y = 51400 _______(2)

Now, multiplying the equation (1) by 55 and (2) by 54, we get.

(54x + 45y = 50400)×55

= 2970x + 2475y = 2772000 _____(3)

(55x + 46y = 51400)×54

= 2970x + 2484y = 2775600 _____(4)

Now, subtracting (3) from (4), we get.

2970x + 2484y = 2775600

2970x + 2475y = 2772000

. - - - ___________________________

. 9y = 3600

___________________________

⇒ 9y = 3600

y = 3600/9

y = 400

Putting the value of y = 400 in (1), we get.

54x + 45y = 50400

54x + (45 × 400) = 50400

54x + 18000 = 50400

54x = 50400 - 18000

54x = 32400

.

x = 600

So, the cost price of a saree is Rs. 600 and the list price of a sweater is Rs. 400