Let C.P. of 1 litre milk be Re. 1

Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.

C.P. of 1 litre mixture = Re.

100
x 1

=
4
125
5

By the rule of alligation, we have:

C.P. of 1 litre of milk
C.P. of 1 litre of water
Re. 1
Mean Price
Re.
4
5
0
4
5
1
5

Ratio of milk to water =
4
:
1
= 4 : 1.
5
5

Hence, percentage of water in the mixture =

1
x 100
%
= 20%.
5

S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.

C.P. of 1 kg of mixture = Rs.

100
x 9.24

= Rs. 8.40
110

By the rule of allilation, we have:

C.P. of 1 kg sugar of 1^st kind
Cost of 1 kg sugar of 2^nd kind
Rs. 9
Mean Price
Rs. 8.40
Rs. 7
1.40
0.60

Ratio of quantities of 1^st and 2^nd kind = 14 : 6 = 7 : 3.

Let x kg of sugar of 1^st be mixed with 27 kg of 2^nd kind.

Then, 7 : 3 = x : 27

x =

7 x 27

= 63 kg.
3

Amount of milk left after 3 operations =

40

1 -
4

3
 litres
40

   =

40 x
9
x
9
x
9

= 29.16 litres.
10
10
10

Let C.P. of 1 litre milk be Re. 1.

S.P. of 1 litre of mixture = Re.1, Gain =
50
%.
3

C.P. of 1 litre of mixture =

100 x
3
x 1

=
6
350
7

By the rule of alligation, we have:

C.P. of 1 litre of water
C.P. of 1 litre of milk
0
Mean Price
Re.
6
7
Re. 1
1
7
6
7

Ratio of water and milk =
1
:
6
= 1 : 6.
7
7

By the rule of alligation, we have:

Strength of first jar
Strength of 2^nd jar
40%
Mean
Strength
26%
19%
7
14

So, ratio of 1^st and 2^nd quantities = 7 : 14 = 1 : 2

Required quantity replaced =
2
3

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

Quantity of water in new mixture =

3 -
3x
+ x

litres
8

Quantity of syrup in new mixture =

5 -
5x

litres
8

3 -
3x
+ x

=

5 -
5x

8
8

5x + 24 = 40 - 5x

10x = 16

x =
8
.
5

So, part of the mixture replaced =

8
x
1

=
1
.
5
8
5

Suppose the can initially contains 7x and 5x of mixtures A and B respectively.

Quantity of A in mixture left =

7x -
7
x 9

litres =

7x -
21
 litres.
12
4

Quantity of B in mixture left =

5x -
5
x 9

litres =

5x -
15
 litres.
12
4

7x -
21

4
=
7

5x -
15
 + 9
4
9

28x - 21
=
7
20x + 21
9

252x - 189 = 140x + 147

112x = 336

x = 3.

So, the can contained 21 litres of A.

Since first and second varieties are mixed in equal proportions.

So, their average price = Rs.

126 + 135

= Rs. 130.50
2

So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

By the rule of alligation, we have:

Cost of 1 kg of 1^st kind
Cost of 1 kg tea of 2^nd kind
Rs. 130.50
Mean Price
Rs. 153
Rs. x
(x - 153)
22.50

x - 153
= 1
22.50

x - 153 = 22.50

x = 175.50

Let the cost of 1 litre milk be Re. 1

Milk in 1 litre mix. in 1^st can =
3
litre, C.P. of 1 litre mix. in 1^st can Re.
3
4
4

Milk in 1 litre mix. in 2^nd can =
1
litre, C.P. of 1 litre mix. in 2^nd can Re.
1
2
2

Milk in 1 litre of final mix. =
5
litre, Mean price = Re.
5
8
8

By the rule of alligation, we have:

C.P. of 1 litre mixture in 1^st can
   C.P. of 1 litre mixture in 2^nd can
3
4
Mean Price
5
8
1
2
1
8
1
8

Ratio of two mixtures =
1
:
1
= 1 : 1.
8
8

So, quantity of mixture taken from each can =

1
x 12

= 6 litres.
2

By the rule of alligation:

Cost of 1 kg pulses of 1^st kind
Cost of 1 kg pulses of 2^nd kind
Rs. 15
Mean Price
Rs. 16.50
Rs. 20
3.50
1.50

Required rate = 3.50 : 1.50 = 7 : 3.