1) Cost of 10 oranges and 12 mangoes is rupees 28 but the cost of 12 oranges and 10 mangoes is rupees one less, find the cost of a mango and an orange.
Answers
Step-by-step explanation:
Let the cost an orange and a mango be x and y respectively.
then, 10x+12y=28. eq1
and, 12x+10y=27. eq2
by adding both equations,we get
22(x+y)=55
x+y=55/22=5/2. eq3
by subtracting both equations
2(y-x)=1
y-x=1/2
x-y=-1/2. eq4
by solving eq 3 and 4
2x=3/2
x=3/4
y=-7/4
Step-by-step explanation:
Given :-
Cost of 10 oranges and 12 mangoes is rupees 28 but the cost of 12 oranges and 10 mangoes is rupees one less,
To find:-
Find the cost of a mango and an orange?
Solution:-
Let the cost of one mango be Rs. X
Let the cost of one orange be Rs. Y
Given that
The Cost of 10 oranges and 12 mangoes=Rs.28
=> 10X + 12Y = 28------------(1)
and
The cost of 12 oranges and 10 mangoes rupees one less the cost of 10 oranges and 12 mangoes
=> 12X + 10 Y = 28-1
=> 12X + 10Y = 27-----------(2)
On adding (1)&(2) then
10X + 12Y = 28
12X + 10Y = 27
(+)
_____________
22X + 22Y = 55
____________
=> 11(2X+2Y ) = 55
=>2X+2Y = 55/11
2X+2Y = 5------------(3)
On Subtracting (2) from (1)
10X + 12Y = 28
12X + 10Y = 27
(-)
_____________
-2X + 2Y = 1 ---------(4)
____________
On adding (3)&(4)
2X+2Y = 5
-2X + 2Y = 1
(+)
___________
0X + 4Y = 6
____________
=> 4Y = 6
=>Y = 6/4
=> Y = 3/2
=> Y = 1.5
On Substituting the value of Y in (3)
2X+2(1.5) = 5
=> 2X+3 = 5
=> 2X= 5-3
=>2X = 2
=> X = 2/2
=> X = 1
Therefore, X =Rs. 1 and Y = Rs. 1.5
Answer:-
The cost of one mango = Rs. 1
The cost of one orange = Rs. 1.5
Check:-
X = Rs. 1 and Y =Rs. 1.5
10X + 12Y
=> 10(1)+12(1.5)
=> 10+18
=> 28
Verified the given relation.
and
12X + 10Y
=> 12(1)+10(1.5)
=> 12+15
=> 27
Verified the given relations in the given problem