Tricks to solve Mixture and Alligation for competitive exam

 

Mixture and Alligation

Question 1: 

 In a mixture of 75 litres, the ratio of milk to water is 2 : 1. The amount of water to be further added to the mixture so as to make the ratio of the milk to water 1 : 2 will be
(1) 45 litres
(2)  60 litres
(3)  75 litres
(4)  80 litres

Solution: 

In 75 litres of the mixture.

Let x litres of water be added,

Short Trick:

3 units = 75 l because 75 l was in ratio 2 : 1 initially.

Question 2:  

A mixture of 40 litres of milk and water contains 10% water. How much water must be added to make 20% water in the new mixture?
(1)  3 litres
(2)  4 litres
(3)  5 litres
(4)  6 litres

Solution 

(8 x 5 = 40 l which is the initial quantity. Hence 1 is also multiplied by 5)

Short Trick:

(40 + x) x 20% = 4 + x
x = 5l

Question 3:  

In three vessels each of 10 l capacity, mixture of milk and water is filled, the ratios of milk and water are 2 : 1, 3 : 1 and 3 : 2 in the three respective vessels, if all the three vessels are emptied into a single large vessel, find the proportion of milk and water in the mixture.
(1)  121 : 59
(2)  123 : 59
(3)  125 : 59
(4)  127 : 59

Solution:

2^nd Method :

L.C.M. of 3, 4 & 5. Hence 3 is multiplied by 4 x 5; 4 is multiplied by 3 x 5; 5 is multiplied by 3 x 4.

Question 4 :

  Vessels A and B contain mixtures of milk and water in the ratios 4 : 5 and 5 : 1 respectively. In what ratio should quantities of mixture be taken from A and B to form a mixture in which milk and water is in the ratio 5 : 4?
(1)  2 : 5
(2)  4 : 3
(3)  5 : 2
(4)  2 : 3

Solution: 

Quantity of milk in vessel A

Quantity of milk in vessel B

Quantity of milk in final mixture


So, mixture of vessels A and B are mixed in ratio of 5 : 2.

2^nd Method :

Question 5: 

50 g of an alloy of gold and silver contains 80% gold (by weight). The quantity of gold, that is to be mixed up with this alloy, so that it may contain 95% gold, is
(1)  200 g
(2)  150 g
(3)  50 g
(4)  10 g

Solution: 

Quantity of gold in the alloy

Let x gm of gold is added, then

Other Method: 

1 unit when multiplied by 50 gives 50g. Hence 3 unit is also multiplied by 50.