Alligation or Mixtures with Explanation

Q1. Find the ratio in which wheat at Rs. 10.80 per kg be mixed with wheat at Rs. 9.30 per kg to get the mixture of worth Rs. 10 per kg?

Answer- Option C

Explanation-

By the rule of alligation, we have:

Required ratio = 80 : 70 = 8 : 7

Q2. The cost of type 1 tea is Rs. 72 per kg and type 2 tea is Rs. 62 per kg. Find the ratio in which both are mixed to obtain the mixture of worth Rs. 64.50 per kg?

Answer- Option D

Explanation-

By the rule of alligation:

Required ratio = 750 : 250 = 3 : 1

Q3. Two container X and Y contain milk and water in the ratio 4 : 3 and 2 :3 respectively. Find the ratio in which the liquids present in both the containers be mixed to get a mixture in container Z having half water and half milk?

Answer- Option A

Explanation-

Let the C.P. of milk be Rs. 1 per litre.
Milk in 1 litre mixture of X =

4 7

litre

Milk in 1 litre mixture of Y =

2 5

litre
Milk in 1 litre mixture of Z =

1 2

litre.
Mean price = Rs.

1 2

.
By the rule of alligation, we have:

Required ratio =

1 10

:

1 14

= 7 : 5

Q4. Spirit and water in two container X and Y are in the ratio 5 : 2 and 7 : 6 respectively. In what ratio these mixtures be mixed to get a new mixture in container Z having water and spirit in the proportion 5 : 8?

Answer- Option B

Explanation-

Let the C.P. of spirit be Rs. 1 per litre.
Spirit in 1 litre mixture of X =

5 7

litre

Spirit in 1 litre mixture of Y =

7 13

litre
Spirit in 1 litre mixture of Z =

8 13

litre.
By the rule of alligation, we have:

Required ratio =

1 13

:

9 91

= 7 : 9.

Q5. Two quality of rice is mixed in the ratio 8 : 7. If the cost of one quality of rice is Rs. 9.30 per kg and the cost of new mixture is Rs. 10 per kg, find the rate per kg of the another quality of rice?

Answer- Option A

Explanation-

Let the rate of the second rice quality be Rs. x per kg.
By the rule of alligation, we have:

(100x - 1000) 70

=

8 7

700x - 7000 = 560
x = Rs. 10.80.

Q6. To obtain a mixture of Rs. 10 a litre, how much water is to be added to 60 litres of milk. The milk is available at 1 litre for Rs. 20

Answer- Option D

Explanation-

C.P. of 1 litre milk = Rs. 20 x

2 3

=

40 3

.

Ratio of water and milk =

8 3

:

32 3

= 1 : 4.

Quantity of water to be added to 60 litres of milk =

1 4

x 60 = 15 litres.

Q7. The rate per litre of milk is Rs. 12. Find the ratio in which water and milk be mixed to get a mixture of worth Rs. 8 per litre.

Answer- Option B

Explanation-

By the rule alligation:

Ratio of water and milk = 4 : 8 = 1 : 2.