Mixture and Alligation | Set 2

Question 1: 30 litres of a mixture of milk and water contains 10% of water, the water to be added, to make the water content 25% in the new mixture. Find how many litres water will be added? 
Solution : Water in the 30 litre of mixture = 30 x 10/100 = 3 litres 
Milk in the mixture = 30 – 3 = 27 litres 
Let x litres of water is mixed. 
Acc. to question 
(3 + x)/(30 + x) = 25/100 
4(3 + x) = 30 + x 
12 + 4x = 30 + x 
3x = 18 
x = 6 
Hence, 6 litres of water to be added in the mixture. 

Alternate :

Question 2: 25000 students appeared in an exam. 60% of the boys and 40% of the girls cleared the examination. If the total percent of students qualifying is 55%, how many girls appeared in the exam? 
Solution : By alligation method 

4 -> 25000 
1 -> 6250 
Hence, number of girls passed in the exam is 6250. 

Question 3: In what ratio must a shopkeeper mix sugar at Rs 30/kg and Rs 32.5/kg, so that by selling the mixture at Rs 34.1/kg he may gain 10%. 
Solution : Acc. to question 
SP of 1 kg of mixture = Rs 34.1 
Profit = 10% = 10/100 = 1/10 
SP = 1 + 10 = 11 unit 
11 units ->34.1 
1 unit -> 3.1 
10 unit -> 31 
We obtain the CP of the mixture Rs 31. 
To obtain the ratio use alligation method 

Hence, the ratio in which he mixed is 3:2

Question 4: Two vessels A and B contain mixture of milk and water in ratios 3:4 and 4:1 respectively. In what ratio should quantities of mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5:2? 
Solution :Acc. to question 

                   Milk        Water        total
Mixture A          3x5     :    4x5      ->    7       LCM(7, 5, 7)=35
Mixture B          4x7     :    1x7      ->    5 
Final mixture      5x5     :    2x5      ->    7

To make quantity equal of both multiply with 7 and 5 respectively. 

                   Milk       Water          
Mixture A          15     :    20      
Mixture B          28     :    7    
Final mixture      25     :    10    

To obtain the ratio in which A and B mixed we apply alligation rule 

Hence, the required ratio is 3:10. 

Question 5: 40 kg of an alloy mixed with 100 kg of alloy B. If alloy A has lead and copper in the ratio 3:2 and alloy B has copper and tin in the ratio 1:3., then the amount of copper in the new alloy is 
Solution :Alloy A 40 kg contains lead and copper in ratio 3:2 
So, 3+2 = 5 
5 unit -> 40 
1 unit -> 8 
2 unit -> 16 
Amount of copper in alloy A is 16 kg. 
Alloy B contains copper and tin in ratio 1:3 
So, 1+3 = 4 
4 unit -> 100 
1 -> 25 
Amount of copper in alloy B is 25 kg 
Hence, amount of copper in the new alloy is 16 + 25 = 41 kg.