In a vessel there is 170 liters of mixture of milk and water in the ratio 12:5. A certain quantity o

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15 Jun 2022 Alligation and Mixture

In a vessel there is 170 liters of mixture of milk and water in the ratio 12:5. A certain quantity of mixture is taken out and same amount of water is added to it, then the ratio of milk and water becomes 48:37. The amount of water in final mixture (in liters) is

OPtion

1) 34
2) 50
3) 96
4) 74
5) 48
6) 72
7) 68
8) 37
9) 130
10) None of these

Solution

In initial mixture of 170 L, Quantity of milk=170*12/17=120 L and water=(170-120)=50 L
Let 'x' L of mixture is taken out and replaced by 'x' L of water
Then, new ratio of milk & water = [120 - x*(12/17)] / [50 - x*(5/17) + x] = 48/37
(170 - x) / (850 + 12x) = 4/37
6290 - 37x = 3400 + 48x
85x = 2890
x = 34
.'. Amount of water in final mixture = 50 - x*(5/17) + x = 50 - 34*(5/17) + 34 = 74 L
Correct Option 4)

Correct Option: 4 Best Solution (2)

G.S.Kantharao   1 year AGO

Out of 170lt mixture Milk and water are =120lt,50lt as per given ratio 12:5
Let x lt be taken.
In x lts 12x/17 is milk, 5x/17 is water. Now when x lts of water is added then,
(120-12x/17):(50-5x/17+x)=48:37
(120-12x/17):(50+12x/17)=48:37
(120*37)-(12*37x/17)=(48*50)+(12*48x/17)
12*85x/17=4440-2400=2040
60x=2040=>x=34
So quantity of water in the second =50+12x/17=50+12*34/17
=50+24=74lt
So my option is 4👈
Alternative method
Total quantity=170lt
It doesn't change in the second case.
So water content in the second =170*37/(48+37)
=170*37/85=74lt.
So my option is 4👈

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Dimple   1 year AGO

As the final quantity of mixture remains same as 170 ltrs and ratio of milk and water is 48:37,
Amount of water in final mixture =170*37/85=74 ltrs

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