A shopkeeper sells article A at 8% profit and
article B at 10% loss, thereby getting a sum
of 1,008. If he sells the article A at 10%
profit and article B at 8% loss, he would have
1,028. Find the cost price of article A and
B to the shopkeeper.
simultaneous linear equation by the elimination method
Answers
Answer:
pata nahi
happy rakshabandhan
Answer:
Let the CP of saree and that of sweater be x and y respectively.
Case 1.
Given that saree is sold at 8% profit
=> SP of saree = x + 8x/100 = 108x/100
Also, sweater is sold at 10% discount
=> SP of sweater = y - 10y/100 = 9y/10
Given that saree and sweater fetch Rs 1008,
108x/100 + 9y/10 = 1008
=> 108x+90y/100 = 1008
=> 108x + 90y = 100800 => 6x + 5y = 5600 => x = 5600-5y/6 (i)
Case 2.
Given that saree is sold at 10% profit
SP of saree = x + 10x/00 = 11x/10
Also, sweater is sold at 8% discount
=> SP of sweater = y - 8y/100 = 92y/100 =
Given that saree and sweater fetch Rs 1028,
11x/10 + 92y/100 = 1028
=> 110x+92y/100 = 1028
=> 110x+92y = 102800
Putting 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 = Rs400
From (i),
x = 5600 - 5*400/6
x = 5600-1200/6
x = 4200/6
=> x = Rs700
Therefore, SP of saree = Rs700
List price of sweater = Rs 400
or
Let the cost price of saree be Rs. 'x' and the list price of sweater be Rs. y.
Therefore,
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)
Situation 2 -
by selling a saree at 10 % profit and a sweater at 8 % discount, the shopkeeper gets Rs. 1028.
⇒ 110x/100 + 92y/100 = 1028
⇒ 11x/10 + 23y/25 = 1028/1
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 = 32400/54
x = 600
So, the cost price of a saree is Rs. 600 and the list price of a sweater is Rs. 400