15 litres of juice contains syrup and water in the ratio of 1:4. If more syrup is added until the ratio
becomes 23 how many litres of juice is now available after the addition of syrup?
Answers
Step-by-step explanation:
no7vi9llUKufl6uzyjx5ihmmlyc[kgh
Answer:
Step-by-step explanation:
Given:-
Two points A(7 , 1) and B(3 , 5)
The point C(x , y) is equidistant from the points A and B.
To Find:-
The relation between x and y.
Concept used:-
The distance between two points A(x₁ , y₁) and B(x₂ , y₂)
The distance between AB is
\sf AB = \sqrt{ (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}AB=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
Solution:-
\sf A(7 , 1) \: and\: C(x , y)A(7,1)andC(x,y)
\sf AB = \sqrt{ (x- 7)^{2} + (y - 1)^{2}}AB=
(x−7)
2
+(y−1)
2
\sf \implies AB = \sqrt{ {x}^{2} + 49 - 14x+ {y}^{2} + 1 - 2y }⟹AB=
x
2
+49−14x+y
2
+1−2y
\sf \implies AB = \sqrt{ {x}^{2} + {y}^{2} - 14x - 2y + 50 }⟹AB=
x
2
+y
2
−14x−2y+50
\sf B( 3, 5) \: and \: C(x , y)B(3,5)andC(x,y)
\sf BC = \sqrt{ (x- 3)^{2} + (y - 5)^{2}}BC=
(x−3)
2
+(y−5)
2
\sf \implies BC = \sqrt{ {x}^{2} + 9 - 6x+ {y}^{2} + 25 - 10y }⟹BC=
x
2
+9−6x+y
2
+25−10y
\sf \implies BC = \sqrt{ {x}^{2} + {y}^{2} - 6x - 10y + 34 }⟹BC=
x
2
+y
2
−6x−10y+34
\sf As, \: C \: is \: equidistant \: from \: A \: and \: BAs,CisequidistantfromAandB
\sf \implies AC = AB⟹AC=AB
\sf \implies \sqrt{ {x}^{2} + {y}^{2} - 14x - 2y + 50 } = \sqrt{ {x}^{2} + {y}^{2} - 6x - 10y + 34 }⟹
x
2
+y
2
−14x−2y+50
=
x
2
+y
2
−6x−10y+34
Squaring on both sides:-
\sf \implies {x}^{2} + {y}^{2} - 14x - 2y + 50 = {x}^{2} + {y}^{2} - 6x - 10y + 34⟹x
2
+y
2
−14x−2y+50=x
2
+y
2
−6x−10y+34
\sf \implies - 14x - 2y + 50 = - 6x - 10y + 34⟹−14x−2y+50=−6x−10y+34
\sf \implies - 14x + 6x - 2y +10y + 50 - 34= 0⟹−14x+6x−2y+10y+50−34=0
\sf \implies - 8x +8y + 16= 0⟹−8x+8y+16=0
Dividing whole equation by 8
\sf \implies - x +y + 2= 0⟹−x+y+2=0
\sf \implies - x +y= - 2⟹−x+y=−2
\sf \implies x - y= 2⟹x−y=2
Therefore, the relation between x and y is:-
\large\dashrightarrow \underline{\boxed{\sf x - y= 2}}⇢
x−y=2