Math, asked by Mohanish98, 9 months ago

Two-fifths of the volume of a mixture of milk and water of ratio 4:3 is
converted into a mixture of ratio 5:3 by the method of replacement with milk.
The 4:3 mixture was prepared from a 4:1 mixture by addition of water. If the
replacement milk volume is 14 litres, what was the volume of the water added
to make the original mixture?
Pick ONE option
A) 12 litres
B) 60 litres
C) 80 litres
D) 24 litres
Clear Selection​

Answers

Answered by amitnrw
4

Given : Two-fifths of the volume of a mixture of milk and water of ratio 4:3 is  converted into a mixture of ratio 5:3 by the method of replacement with milk.  Replacement milk volume is 14 litres

The 4:3 mixture was prepared from a 4:1 mixture by addition of water.

To Find : volume of the water added  to make the original mixture

A) 12 litres

B) 60 litres

C) 80 litres

D) 24 litres

Solution:

Original Mixture  4: 1

MIlk = 4X litre

Water = X  litre

Water added = Y litre

=> Milk = 4X ,  water = X + Y

Ratio = 4 : 3

=> 4X / ( X + Y) = 4/3

=> 3X = X + Y

=> 2X = Y  

Milk = 4X

Water = 3X

Mixture = 7X

Two-fifths of the volume of a mixture of milk

= (2/5)7X

= 14X/5

MILK = 8X/5

WATER = 6X/5

converted into a mixture of ratio 5:3 by the method of replacement with milk. replacement milk volume is 14 litres,

14 litre has   (4/7)14 = 8 litre milk  and 6 litre water

MILK  = 8X/5   - 8 + 14  =  8X/5 + 6  = (8X + 30)/5

WATER = 6X/5  -  6  = (6X - 30)/5

Ratio = 5 : 3

=>  (8X + 30) / (6X - 30)  = 5/3

=> 24X + 90 = 30X - 150

=> 6X = 240

=> X = 40

Original mixture has 40 Litre Water

Info :

Original  mixture       MILK 160     WATER  40    Ratio 4 : 1

Water Added  = 80 LITRE

Now  Mixture           MILK 160     WATER  120    Ratio 4 : 3

2/5 of Mixture          MILK 64      WATER  48     Ratio 4 : 3

replacement with 14 Litre milk  

14 Litre has   8 LITRE MILK  and 6 LITRE WATER

FINAL MIXTURE    64 - 8 + 14 = 70    WATER = 48 - 6 = 42

70 : 42   =  5 : 3

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