Question

The contents of two vessels containing water and milk in the ratio 1 : 2 and 2 : 5 are mixed in the ratio 1 : 4 The resulting mixture will have water and milk in the ratio

Answer 1

Answer:

Let the first mixture be A.

Then A≡water:milk=1:2, &

Let the second mixture be B.

Then B≡water:milk=2:5.

So in A the amount of milk=

1+2

2

part=

3

2

part

and in B the amount of milk=

2+5

5

part=

7

5

part.

Similarly, in A the amount of water=

1+2

1

part=

3

1

part

and in B the amount of water=

2+5

2

part=

7

2

part.

Now, in the new mixture A:B=1:4.

So the quantity of mixture A=1×A=1×

3

2

part milk==

3

2

part milk and

1×

3

1

patrt water=

3

1

part of water.

Similarly, the quantity of mixture B=4×B=4×

7

5

part milk==

7

20

part milk and

4×

7

2

part water=

7

8

part of water.

Then the total quantity of milk in the new mixture=

3

2

+

7

4

part

=

21

74

part .

Again the total quantity of water in the new mixture=

3

1

+

7

8

part

=

21

31

part .

So, in the new mixture,

water : milk=

21

31

:

21

74

=31 : 74