Ratio, Proportion
- One morning after purchasing 6 litres of milk from a milk man , a householder found that the weight of this quantity of milk was 6 .144 kg . If one litre of the pure milk weighs 1 .032 kg and that of one litre of the pure water 1 kg . then how much water was added to milk ?
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Weight of 1 kg of impure milk ; 6. 144 = 1.024 kg 6
Weight of water6 – 1.024 " 6 1.032
= 6 – 5 .9 5
= 0.05 kgCorrect Option: C
Weight of 1 kg of impure milk ; 6. 144 = 1.024 kg 6
Weight of water6 – 1.024 " 6 1.032
= 6 – 5 .9 5
= 0.05 kg
- A , B a nd C go into a business as partners with the agreement that their shares of pro fit will be in the
proportion of their capitals . If A ’s capital : B ’s capital = 2:3, and B ’s capital : C ’s capital = 2 : 5 , find their shares in a profit of Rs . 3250.
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A : B = 2 : 3 = 4 : 6
B :C = 2 : 5 = 6 : 1 5
A : B : C = 4 : 6 : 1 5
A + B + C = 4 + 6 + 15 = 25A’s share = 4 " 3250 = Rs . 520 25 B’s share = 6 " 3250 = Rs . 780 25 C’s share = 15 " 3250 = Rs . 1950 25 Correct Option: A
A : B = 2 : 3 = 4 : 6
B :C = 2 : 5 = 6 : 1 5
A : B : C = 4 : 6 : 1 5
A + B + C = 4 + 6 + 15 = 25A’s share = 4 " 3250 = Rs . 520 25 B’s share = 6 " 3250 = Rs . 780 25 C’s share = 15 " 3250 = Rs . 1950 25
- Three vessels of equal volumes contain water and syrup in the ratio 4 : 1 , 5 : 2 and 7 : 3 respectively . When they are thoroughly mixed together in a large vessel, find the resulting ratio of water and syrup in the mixture . (Assume that in the mixture total volume remains unaltered ).
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Let the capacity of each vessel be x litres.
∴ Ratio= 4x ) 5x ) 7x : x ) 2x ) 3x 5 7 10 5 7 10 = 56x ) 50x ) 49x : 14x ) 20x ) 21x 70 70 = 155x : 55x 70 70
= 31 : 11Correct Option: C
Let the capacity of each vessel be x litres.
∴ Ratio= 4x ) 5x ) 7x : x ) 2x ) 3x 5 7 10 5 7 10 = 56x ) 50x ) 49x : 14x ) 20x ) 21x 70 70 = 155x : 55x 70 70
= 31 : 11
- 3 litres of a mixture containing wine and water in the ratio 3 : 7 and 4 litres of another mixture containing wine and water in the ratio 3 : 5 are mixed together. What is the ratio of wine and water in the resulting mixture ?
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In 3 litres of mixture ,
Wine = 3 " 3 ; 9 litre 10 10 Water = 7 " 3 ; 21 litre 10 10
In 4 litres of mixture ,Wine = 3 " 4 ; 3 litres 8 2 Water = 5 " 4 ; 5 litres 8 2
In resulting mixture ,
Wine : Water= 9 ) 3 : 21 ) 5 10 2 10 2
= 24 : 46 = 12 : 23Correct Option: B
In 3 litres of mixture ,
Wine = 3 " 3 ; 9 litre 10 10 Water = 7 " 3 ; 21 litre 10 10
In 4 litres of mixture ,Wine = 3 " 4 ; 3 litres 8 2 Water = 5 " 4 ; 5 litres 8 2
In resulting mixture ,
Wine : Water= 9 ) 3 : 21 ) 5 10 2 10 2
= 24 : 46 = 12 : 23
- The sum of the squares of two positive numbers is greater than their product by 2 8 . If the ratio of the numbers 2 : 3 , find th e numbers .
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Let the numbers be 2x and 3x.
∴ (3x)2 + (2x)2 2 – 2x × 3x = 28
⇒ 13x2 – 6x2 = 28
⇒ 7x2 = 28⇒ x2 = 28 ; 4 7
⇒ x = √4 = 2
∴ Numbers are : 4 and 6Correct Option: A
Let the numbers be 2x and 3x.
∴ (3x)2 + (2x)2 2 – 2x × 3x = 28
⇒ 13x2 – 6x2 = 28
⇒ 7x2 = 28⇒ x2 = 28 ; 4 7
⇒ x = √4 = 2
∴ Numbers are : 4 and 6