The ratio of milk and water in a vessel is 5:3.How much part of a mixture is replaced by 14 1/2% part of water so that the ratio of new mixture becomes 3 : 5?
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Answer:
Thus 6.348 x or @ 81 % of solution to be replaced with14 1/2 % water
Step-by-step explanation:
Assume milk=5x litres and water is 3x litres in this mixture-1
Total mixture=5x+3x=8x
Now let y litre mixture is removed and y*(14 1/2) =y*29/(2*100)
=29y/200 litre water is added
Now In the Resulting miture
Milk=(8x-y)*5/8=(40x-5y)/8........................(1)
and water= (8x-y)*3/8+29y/200
Water=1/200{ 75(8x-y) +29y}
Water=( 600x-46y)/20 litre............................(2)
As per given new milk : water=3:5
(40x-5y)/8 : (600x-46y)20 :: 3:5
5/8*(40x-5y)=3/20(600x-46y)
(200x-25y)/8=(1800x-138y)/20
4000x-500y=14400x-1104y
10400x=1604y
y=10400x/1604=6.48 x
Thus 6.48 x of 8 x
=6.48*100/8=81 %
Thus 6.348 x or @ 81 % of solution to be replaced with14 1/2 % water
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