Mixture and Alligation Questions & Answers
11. In what ratio should wheat at Rs12.60 per kg be mixed with wheat at Rs. 14.60 per kg so that the mixture
be worth Rs.13 per kg ?
Explanation: So the ratio will be :
1460 - 1300 : 1300-1260
=> 160 : 40 => 4:1
12. How many kg of dal at Rs.8.40 per kg be mixed with32 kg of dall at Rs10.20 per kg to get a mixture worth
Rs.9.60 per kg?
Explanation: By the rule of allegation ,we have
C.P. of 1 kg of 1st kind dal = 840
C.P. of 1 kg of 2nd kind dal = 1020
Price of 1kg of mixture = 960
So, 1020-960 : 960-840 => 60:120 => 1:2
=> Quantity of 1st kind dall:32 = 1:2
Quantity of 1st kind dall =32 *1/2 = 16
13. How many litres of water should be added to a 30 litre mixture of milk and water containing milk and
water in the ratio of 3:7 such that the resultant mixture has 40% water in it?
Explanation: 60 litres of the mixture has milk and water in the ratio 3:7.
i.e. the solution has 21 litres of milk and 9 litres of water.
When you add more water, the amount of milk in the mixture remains constant at 21 litres.
In the first case, before addition of further water, 21 litres of milk accounts for 70% by volume.
After water is added, the new mixture contains 60% milk and 40% water.
Therefore, the 21 litres of milk accounts for 60% by volume.
14. Suprith bought 40 kg of rava at the rate of Rs.8.50 per kg and 55 kg at the rate of Rs.8.75 per kg. He
mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit at the cost
Explanation: CP = 40 × 8.50 + 55 ×8.75
= 340 + 481.25
Profit = 40%
SP= (100 +40) /100 × c.p
= 1.4 × 821.25
Total quantity = 40 + 55 = 95 kg
SP per kg =(1.4 x821.25) / 95} = 12
15. How many kgs of Ponni rice costing Rs.21/kg should a shopkeeper mix with 12.5 kgs of ordinary rice
costing Rs.12 per kg so that he makes a profit of 25% on selling the mixture at Rs.20/kg?
Explanation: As the trader makes 25% profit by selling the mixture at Rs.20/kg, his cost per kg of the mixture = Rs.16/kg.
C.P of 1 kg of rice of 1st kind = Rs. 21
C.P of 1 kg of rice of 2nd kind = Rs. 12
Mean price = Rs. 16
By the rule of alligation
Let the amount of ponni rice being mixed be x kgs
4:5 = x : 12.5
X = 10 kg
16. A container contains 55 litres of milk. From this container 5.5 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
Explanation: Where x is the initial quantity of milk in the cask y is the quantity of milk withdrawn in each process and n is the number of processes.
number of times repeated=3
Hence from the above rule it can be say that, Formula,=[a(1-b/a)n ]
Quantity of milk left after the 3rd operation =55*((55-5.5)/55) ^3 =40.09litres
17. Two vessels A and B contain sugar and rava in the ratio 4 : 3 and 2 : 3 respectively. Find the ratio in
which these mixtures be mixed to obtain a new mixture in vessel C containing sugar and rava in the ratio 1 :
Explanation: Let Cost Price(CP) of 1 kg sugar be Rs.1
Quantity of sugar in 1kg mixture from vessel A=4/7
Cost Price(CP) of 1kg mixture from vessel A = Rs. =4/7
Quantity of sugar in 1 kg mixture from vessel B =2/5
Cost Price(CP) of 1 kg mixture from vessel B = Rs. =2/5
Quantity of sugar to be obtained in 1 kg mixture from vessel C=1/2
Cost Price(CP) of 1 kg mixture from vessel C(Mean Price) = Rs.=1/2
Mixture from Vessel A : Mixture from Vessel B
18. The cost of Type 1 material is Rs. 50per kg and Type 2 material is Rs.75 per kg. If both Type 1 and Type
2 are mixed in the ratio of 3:2 then what is the price per kg of the mixed variety of material?
Explanation: Cost Price (CP) of Type 1 material is Rs. 50 per kg
Cost Price (CP) of Type 2 material is Rs. 75 per kg
Let Cost Price(CP) of resultant mixture be Rs.x per kg
Type 1 material : Type 2 material = 3/2
75-x : x-50 =3/2
X = 60
19. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
Explanation: By the rule of alligation:
Cost of 1 kg pulses of 1st kind = Rs 15
Cost of 1 kg pulses of 2nd kind Rs. 20
Mean Price = Rs. 16.50
Required rate = 3.50 : 1.50 = 7 : 3.
20. A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
Explanation: Amount of milk left after 3 operations = ( 40 (1 - ((4/10)^3)) => 29.16 litres.