The cost of 4 kg onion, 3 kg wheat
and 2 kg rice is `320. The cost of 2kg onion,
4 kg wheat and 6 kg rice is `560. The cost
of 6 kg onion, 2 kg wheat and 3 kg rice is
`380. Find the cost of each item per kg?
Answers
Answer: 70
Step-by-step explanation:
Let cost of each Kg of onion = Rs x
Cost of each Kg of wheat = Rs y
And cost of each Kg of rice = Rs z
Given that cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60
So
4x + 3y + 2 z = 60 …(1)
Given that The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90
So
2x + 4y + 6z = 90
Divide equation by 2 we get
X + 2y + 3z = 45 … (2)
Given that The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70.
So
6x + 2y + 3z = 70 … (3)
So our set of equation is
4x + 3y + 2 z = 60
2x + 4y + 6z = 90
6x + 2y + 3z = 70
Step-by-step explanation:
Given :-
The cost of 4 kg onion, 3 kg wheat and 2 kg rice is `320. The cost of 2kg onion, 4 kg wheat and 6 kg rice is `560. The cost of 6 kg onion, 2 kgwheat and 3 kg rice is `380
To find :-
Find the cost of each item per kg?
Solution :-
Given that :
Let the cost of one kg of onions = Rs. X
Let the cost of one kg of wheat = Rs. Y
Let the cost of one kg of rice = Rs. Z
Given that
The cost of 4 kg onion, 3 kg wheat and 2 kg rice = Rs. 320.
= 4X + 3Y + 2Z= 320 ------------(1)
The cost of 2kg onion, 4 kg wheat and 6 kg rice = Rs.560.
= 2X + 4Y + 6Z = 560 ----------(2)
On multiplying with 2 then
= 4X + 8Y + 12Z = 1120 ------(3)
The cost of 6 kg onion, 2 kgwheat and 3 kg rice = Rs.380
= 6X + 2Y + 3Z = 380 ---------(4)
On Subtracting (1) from (3)
4X + 8Y + 12Z = 1120
4X + 3Y + 2Z= 320
(-)
________________
0+5Y +10Z = 800
________________
=> 5Y+10Z = 800
=> 5(Y+2Z) = 800
=> Y+2Z = 800/5
=>Y+2Z = 160
=> Y = 160-2Z---------(5)
2X + 4Y + 6Z = 560 ----------(2)×3
6X+12Y+18Z=1680---------(6)
On subtracting (4) from (6)
6X+12Y+18Z=1680
6X + 2Y + 3Z = 380
(-)
________________
0+10Y+15Z = 1300
________________
=> 10Y+15Z = 1300
=>5(2Y+3Z) = 1300
=> 2Y+3Z = 1300/5
=> 2Y+3Z = 260------------(7)
On Substituting the value of Y from (5) in (7)
=> 2(160-2Z)+3Z = 260
=> 320-4Z +3Z = 260
=> 320-Z = 260
=> Z = 320-260
=> Z = 60 ------------(8)
On Substituting the value of Z in (5)
=> Y = 160-2(60)
=> Y = 160-120
=> Y = 40-----------(9)
On Substituting these values of Y and Z in (1) then
4X + 3Y + 2Z= 320
=> 4X+3(40)+2(60) = 320
=> 4X+120+120=320
=> 4X+240 = 320
=> 4X = 320-240
=> 4X = 80
=> X = 80/4
=> X = 20
Therefore, X = Rs. 20 , Y = Rs. 40 ,Z = Rs. 60
Answer:-
The cost of one kg of onions = Rs. 20
The cost of one kg of wheat = Rs. 40
The cost of one kg of rice = Rs. 60
Check:-
The cost of 4 kg onion, 3 kg wheat and 2 kg rice
= (4×20)+(3×40)+(2×60)
= 80+120+120
= Rs. 320.
and
The cost of 2kg onion, 4 kg wheat and 6 kg rice =
= (2×20)+(4×40)+(6×60)
= 40+160+360
=Rs.560.
and
The cost of 6 kg onion, 2 kgwheat and 3 kg rice =
=(6×20)+(2×40)+(3×60)
= 120+80+180
=Rs.380
Verified the given relations in the given problem.