A mixture Contains X litre milk And Y litre Water. If 18Litre of mixture is taken out and replaced with water such that ratio of milk and water becomes 3:1 But If 60 Litre of mixture is taken out and replaced with water then ratio of milk and water becomes 2:3.
Find X?
Answers
Answer:
97.2
Step-by-step explanation:
x - milk
y - water
total liquid = x + y
1) 18l mixture taken out, and added 18l water
18l mixture = 18x/(x + y) milk + 18y/(x + y) water
new mixture
milk = x - 18x/(x + y)
water = y - 18y/(x +y) + 18
(x^2 + xy - 18x)/(x + y) : (y^2 + xy - 18y + 18x + 18y)/(x + y) = 3:1
=>(x^2 + xy - 18x) = 3(y^2 + xy + 18x) -----(1)
2) 60l mixture taken out, and added 60l water
60l mixture = 60x/(x + y) milk + 60y/(x + y) water
new mixture
milk = x - 60x/(x + y)
water = y - 60y/(x +y) + 60
(x^2 + xy - 60x)/(x + y) : (y^2 + xy - 60y + 60x + 60y)/(x + y) = 2:3
=> 3(x^2 + xy - 60x) = 2(y^2 + xy + 60x)
=> 3(x^2 + xy - 18x - 42x) = 2(y^2 + xy + 60x)
=> 3(3(y^2 + xy + 18x) - 42x) = 2(y^2 + xy + 60x) -----(from (1))
=> 9y^2 + 9xy + 162x - 126x = 2y^2 + 2xy + 120x
=> 7y^2 + 7xy - 84x = 0
=> y^2 + xy - 12x = 0
putting in (1)
=>(x^2 + xy - 18x) = 3(y^2 + xy + 18x) -----(1)
=>(x^2 + xy - 18x) = 3(y^2 + xy -12x + 12x + 18x)
=>(x^2 + xy - 18x) = 3(0 + 12x + 18x)
=> x^2 + xy - 18x = 90x
=> x + y - 18 = 90
=> x + y = 108
=> y = 108 - x
putting y in (2)
=> y^2 + xy - 12x = 0
=> (108 -x)^2 + x (108-x) -12x = 0
=> 108^2 - 216x + x^2 + 108x -x^2 -12x = 0
=> 108^2 - 120x = 0
=> x = 108 * 108/120
=> x = 97.2