A milk vender has 2 cans of milk. the 1st contains 25% water and the rest milk. the second contains 50% water. how much milk should be mixed from each of the containers so as to get 12 liters of milk such that the ratio of water to milk is 3:5 ? (a) 4l, 8l
Answers
Answer : Option C
Explanation :
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Solution 1
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Let x and (12-x) litres of milk be mixed from the first and second container respectively
Amount of milk in x litres of the the first container = .75x
Amount of water in x litres of the the first container = .25x
Amount of milk in (12-x) litres of the the second container = .5(12-x)
Amount of water in (12-x) litres of the the second container = .5(12-x)
Ratio of water to milk = [.25x + .5(12-x)] : [.75x + .5(12-x)] = 3 : 5
⇒(.25x+6−.5x)(.75x+6−.5x)=35⇒(6−.25x)(.25x+6)=35⇒30−1.25x=.75x+18⇒2x=12⇒x=6⇒(.25x+6−.5x)(.75x+6−.5x)=35⇒(6−.25x)(.25x+6)=35⇒30−1.25x=.75x+18⇒2x=12⇒x=6
Since x = 6, 12-x = 12-6 = 6
Hence 6 and 6 litres of milk should mixed from the first and second container respectively
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Solution 2
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Let cost of 1 litre milk be Rs.1Milk in 1 litre mix in 1st can = 34 litreCost Price(CP) of 1 litre mix in 1st can = Rs.34Milk in 1 litre mix in 2nd can = 12 litreCost Price(CP) of 1 litre mix in 2nd can = Rs.12Milk in 1 litre of the final mix =58Cost Price(CP) of 1 litre final mix = Rs.58=> Mean price = 58Let cost of 1 litre milk be Rs.1Milk in 1 litre mix in 1st can = 34 litreCost Price(CP) of 1 litre mix in 1st can = Rs.34Milk in 1 litre mix in 2nd can = 12 litreCost Price(CP) of 1 litre mix in 2nd can = Rs.12Milk in 1 litre of the final mix =58Cost Price(CP) of 1 litre final mix = Rs.58=> Mean price = 58
By the rule of alligation, we can write as
=> mix in 2nd can :mix in 1st can = 1/8 : 1/8 = 1:1
ie, from each can, 12×12=6 litre should be taken