Averages Mixture Allegation Notes
Average:
Average is a very simple but effective way of representing an entire group by a single value.
"Average " of a group is defined as
Average = Sum of all items in the group/Number of items in the group
A student expresses his score in the exams by giving "average" percentage in all paper together rather than scores in individual papers.
Similarly, if there are 60 students in a class, instead of talking of the height of each individual student, we can talk of "average" height of the class.
Note:- Average of any number of quantities will always be higher than the lowest value and lower than the higher value of items whose average is being taken.
Mixture- Allegation:
Mixing of two or more types of qualities of things produces a mixture. When two items of different qualities are thus mixed, the quality of the resultant mixture lies in between the qualities of the original constituent items, i.e., it will be higher than the lowest quality and lower than the highest quality of the items being mixed.
Similarly, if two types of a product of different prices per unit are mixed, the unit price of the resultant mixture will lie between the prices of the two types that form the mixture.
The following Rule of Allegation connecting quantities and mixture will be useful in problems on mixtures and weighted averages.
Quantity of cheaper = Rate of dearer -Average Rate
Quantity of dearer Average Rate - Rate of Cheaper
Worked out Examples:
1) The daily temperature in a week from monday to sunday is 42°C, 43° C, 42°C, 41°C, 40°C, 44°C, 42°C respectively. What is the daily average temperature ?
Sol:-
Average Temperature = Sum of the temperatures
Number of Days
= 42+43+42+41+40+44+42
7
= 42°C
2) The cost of none quality of rice is Rs. 12 per kg and that of other quality is Rs. 16 per kg. If six kilograms of the first quality and four kilograms of the second quality are mixed, what is the average cost of the mixture ?
Sol:-
The cost of 4 kg of first quality of rice = 6x12 = Rs.72
The cost of second quality of rice = 4x16= Rs.64
Total cost of 10 kgs = 72+64 = Rs.136
Average cost of the mixture = 136/10 = Rs.13.60
Note:- This average, as detailed in the above example is called " the Weighted Average". The price of rice is "weighted" by the quantity purchased to get "Weighted Average Price " of rice.
3) How much quantity of tea costing Rs.120 a kg be mixed with 6 kgs of tea costing Rs. 180 a kg such that the mixture costs Rs. 160 a kg ?
sol:-
Applying the rule of allegation
Quantity of Rs.120 a kg = 180-160
Quantity of Rs.180 a kg 160-120
= 20/40= 1/2
Therefore the quantity of tea costing Rs.120 a kg that is mixed = (1/2)6 = 3 kg
Important Links:
Average:
Average is a very simple but effective way of representing an entire group by a single value.
"Average " of a group is defined as
Average = Sum of all items in the group/Number of items in the group
A student expresses his score in the exams by giving "average" percentage in all paper together rather than scores in individual papers.
Similarly, if there are 60 students in a class, instead of talking of the height of each individual student, we can talk of "average" height of the class.
Note:- Average of any number of quantities will always be higher than the lowest value and lower than the higher value of items whose average is being taken.
Mixture- Allegation:
Mixing of two or more types of qualities of things produces a mixture. When two items of different qualities are thus mixed, the quality of the resultant mixture lies in between the qualities of the original constituent items, i.e., it will be higher than the lowest quality and lower than the highest quality of the items being mixed.
Similarly, if two types of a product of different prices per unit are mixed, the unit price of the resultant mixture will lie between the prices of the two types that form the mixture.
The following Rule of Allegation connecting quantities and mixture will be useful in problems on mixtures and weighted averages.
Quantity of cheaper = Rate of dearer -Average Rate
Quantity of dearer Average Rate - Rate of Cheaper
Worked out Examples:
1) The daily temperature in a week from monday to sunday is 42°C, 43° C, 42°C, 41°C, 40°C, 44°C, 42°C respectively. What is the daily average temperature ?
Sol:-
Average Temperature = Sum of the temperatures
Number of Days
= 42+43+42+41+40+44+42
7
= 42°C
2) The cost of none quality of rice is Rs. 12 per kg and that of other quality is Rs. 16 per kg. If six kilograms of the first quality and four kilograms of the second quality are mixed, what is the average cost of the mixture ?
Sol:-
The cost of 4 kg of first quality of rice = 6x12 = Rs.72
The cost of second quality of rice = 4x16= Rs.64
Total cost of 10 kgs = 72+64 = Rs.136
Average cost of the mixture = 136/10 = Rs.13.60
Note:- This average, as detailed in the above example is called " the Weighted Average". The price of rice is "weighted" by the quantity purchased to get "Weighted Average Price " of rice.
3) How much quantity of tea costing Rs.120 a kg be mixed with 6 kgs of tea costing Rs. 180 a kg such that the mixture costs Rs. 160 a kg ?
sol:-
Applying the rule of allegation
Quantity of Rs.120 a kg = 180-160
Quantity of Rs.180 a kg 160-120
= 20/40= 1/2
Therefore the quantity of tea costing Rs.120 a kg that is mixed = (1/2)6 = 3 kg
Important Links:
- Marketing and Business Knowledge Notes for Bank Tests
- Computer Knowledge Notes for Bank Tests
- Percentages Profit & Loss Notes for Competitive Exams
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