Ratio, Proportion
- Find the proportion in which three types of sugar at ₹ 12, ₹ 14 and ₹ 20 may be mixed so as to obtain a
mixture worth 15 per kg ?
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Required proportion = 5 : 5 : (3 + 1 ) o r 5 : 5 : 4 .
Note : We can find other alternatives too by adding multiples of the quantities obtained at I and II. This will give us infinite number of alternatives. Care must be taken not to mix up quantities of one pair with another
For example ,
Correct Option: B
Required proportion = 5 : 5 : (3 + 1 ) o r 5 : 5 : 4 .
Note : We can find other alternatives too by adding multiples of the quantities obtained at I and II. This will give us infinite number of alternatives. Care must be taken not to mix up quantities of one pair with another
For example ,
- In what proportion may three kinds of rice bought at ₹ 6 , ₹ 10 and ₹ 14 be mixed to produce a mixture
which would earn 40% on selling it at ₹ 11.20 per kg ?
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SP o f mixture
= ₹ 11.20 per kg .
Profit = 40% .CP of mixture ; 11.20 " 100 140
= ₹ 8 per kg .
R e q u ire d ra tio
= 8 : 2 : 2 or 4 :1 : 1 .Correct Option: A
SP o f mixture
= ₹ 11.20 per kg .
Profit = 40% .CP of mixture ; 11.20 " 100 140
= ₹ 8 per kg .
R e q u ire d ra tio
= 8 : 2 : 2 or 4 :1 : 1 .
- In what proportion may three kinds of tea prices at ₹ 80, ₹ 70 and ₹ 50 per kg be mixed to produce a mixture worth ₹ 60 per kg?
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Write the prices in ascending or descending order as shown below :
Make pairs by choosing one from each side of the mean price and apply A llig a tio n Rule . The n a d d
the quantity obtained under each price . This will give the ratio in which the ingredients should be mixed .
So , Required ratio
= 10 : 10 : 30 or 1 :1 : 3 .Correct Option: D
Write the prices in ascending or descending order as shown below :
Make pairs by choosing one from each side of the mean price and apply A llig a tio n Rule . The n a d d
the quantity obtained under each price . This will give the ratio in which the ingredients should be mixed .
So , Required ratio
= 10 : 10 : 30 or 1 :1 : 3 .
- In what ratio a trader should mix two varieties of tea one at ₹ 62 per kg and other at ₹ 72 per kg in order to obtain the mixture worth ₹ 65 per kg ?
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C.P. of 1 kg tea of Ist quality = ₹ 62
C.P. of 1 kg tea of 2nd quality= ₹ 72.
Mean Price = ₹ 65
Using Alligation Rule ,Quantity of 1st tea ; d − m ; 7 Quantity of 2nd tea m − c 3
Therefore , they must be mixed in the ratio of 7 : 3 .
[Since this problem is the inverse of above type problem , it is called ‘Alligation alternate ’].Correct Option: B
C.P. of 1 kg tea of Ist quality = ₹ 62
C.P. of 1 kg tea of 2nd quality= ₹ 72.
Mean Price = ₹ 65
Using Alligation Rule ,Quantity of 1st tea ; d − m ; 7 Quantity of 2nd tea m − c 3
Therefore , they must be mixed in the ratio of 7 : 3 .
[Since this problem is the inverse of above type problem , it is called ‘Alligation alternate ’].
- A shopkeeper mixes 12 kgs of rice at ₹ 8 per kg with 6 kgs of rice at 10 per kg . Find the cost per kg of the mixture .
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Total quantity of the mixture
= 12 + 6 = 18 kgs .
Cost of 12 kgs of rice at ₹ 8 per kg = ₹ (12 × 8) = ₹ 96
Cost of 6 kgs of rice at ₹ 10 per kg
= ₹ (6 × 10) = ₹ 60
∴ Total cost of 18 kgs of the mixture
= ₹ (96 + 60) = ₹ 156
∴ Cost per kg of the mixture= Rs. 156 ; ₹ 8.67 per kg 18 kgs
[Because cost of the mixture lies somewhere in the middle of ₹ 8 and ₹ 10, so this type of problem is known as ‘Alligation medial’].Correct Option: A
Total quantity of the mixture
= 12 + 6 = 18 kgs .
Cost of 12 kgs of rice at ₹ 8 per kg = ₹ (12 × 8) = ₹ 96
Cost of 6 kgs of rice at ₹ 10 per kg
= ₹ (6 × 10) = ₹ 60
∴ Total cost of 18 kgs of the mixture
= ₹ (96 + 60) = ₹ 156
∴ Cost per kg of the mixture= Rs. 156 ; ₹ 8.67 per kg 18 kgs
[Because cost of the mixture lies somewhere in the middle of ₹ 8 and ₹ 10, so this type of problem is known as ‘Alligation medial’].
