Alligation or Mixture

Q.1

. In what ratio must rice at Rs. 9.30 per kg be mixed with rice at Rs. 10.80 per kg so that the mixture be worth Rs. 10 per kg ?

1:8

1:7

7:8

8:7

Explanation :
By the rule of alligation, we have: C.P. of 1 kg rice of 1st kind (in paise)
C.P. of 1 kg rice of 2nd kind (in paise)

Q.2

How much water must be added to 60 litres of milk at 1 ½ litres for Rs. 2 So as to have a mixture worth Rs.10 2/3 a litre ?

25 litre

10 litre

15 litre

20 litre

Explanation :
. C.P. of 1 litre of milk = Rs. (20 x 2/3) = Rs. 40/3

Q.3

. In what ratio must water be mixed with milk to gain 20 % by selling the mixture at cost price?

1/6:5/6

1:6

5:6

6/1:6/5

Explanation :
Let C.P. of milk be Re. 1 per litre.
Then, S.P. of 1 litre of mixture = Re. 1. Gain obtained = 20%.
C.P. of 1 litre of mixture = Rs.[(100/120)* 1]=Rs.5/6 By the rule of alligation, we have:

Q.4

How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?

10.6 Kg

10.8 Kg

10.0 Kg

10.1 Kg

Explanation :
. S.P. of 1 kg mixture = Rs. 7.20,Gain = 20%.
C.P. of 1 kg mixture = Rs.[(100/120)*7.20]=Rs. 6.
By the rule of alligation, we have:

Q.5

The milk and water in two vessels A and B are in the ratio 4 : 3 and 2: 3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?

1:7

1:5

5:7

7:5

Explanation :
. Let the C.P. of milk be Re. 1 per litre
Milk in 1 litre mixture of A = 4/7litre; Milk in 1 litre mixture of B = 2/5 litre; Milk in 1 litre mixture of C = ½ litre
C.P. of 1 litre mixture in A = Re .4/7; C.P. of 1 litre mixture in B = Re.2/5 Mean price = Re.1/2
By the rule of alligation, we have:

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