A mixture contains milk and water in the ratio 5:3, respectively. 25% of the mixture is taken out and replaced with same amount of water. In the remaining mixture, 5 litres each of milk and water is added such that the ratio of milk to water in the mixture becomes 8:9. Find the initial quantity of mixture.
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Answer:
Let the vessel contains 8 litres of liquid.
Let x litres of this liquid be replaced with water
when x litre of mixture is taken out it means
8
5x
litre milk and
8
3x
litre water taken out
Quantity of water in new mixture =(3−
8
3x
+x)litres
Quantity of milk in new mixture =(5−
8
5x
)litres
∴(3−
8
3x
+x)=(5−
8
5x
)
⇒5x+24=40−5x
⇒10x=16
∴x=
5
8
So, part of the mixture replaced =(
5
8
×
8
1
)=
5
1
.
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