Ratio, Proportion
- Three utensils contain equal quantity of mixtures of milk and water in the ratio 6 : 1, 5 : 2 and 3 : 1 respectively. If all the solutions are mixed together, the ratio of milk and water in the final mixture is
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Let each vessel contain 1 litre of mixture.
= 6 + 5 + 3 7 7 4 = 24 + 20 + 21 = 65 litre 28 28
Total quantity of water= 1 + 2 + 1 7 7 4 = 4 + 8 + 7 = 19 litre 28 28 ∴ Required ratio = 65 : 19 28 28
= 65 : 19Correct Option: B
Let each vessel contain 1 litre of mixture.
= 6 + 5 + 3 7 7 4 = 24 + 20 + 21 = 65 litre 28 28
Total quantity of water= 1 + 2 + 1 7 7 4 = 4 + 8 + 7 = 19 litre 28 28 ∴ Required ratio = 65 : 19 28 28
= 65 : 19
- Two alloys contain tin and iron in the ratio of 1 : 2 and 2 : 3. If the two alloys are mixed in the proportion of 3 : 4 respectively (by weight), the ratio of tin and iron in the newly formed alloy is :
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Let 3kg of first alloy and 4 kg of second alloy be mixed together.
∴ In 3 kg of mixture,
Tin = 1 kg.
Iron = 2 kg.
In 4 kg of mixture,Tin = 2 × 4 = 8 = 1.6 kg. 5 5 Iron = 3 × 4 = 12 = 2.4 kg. 5 5
∴ Required ratio
= (1 + 1.6) : (2 + 2.4) = 2.6 : 4.4
= 13 : 22Correct Option: B
Let 3kg of first alloy and 4 kg of second alloy be mixed together.
∴ In 3 kg of mixture,
Tin = 1 kg.
Iron = 2 kg.
In 4 kg of mixture,Tin = 2 × 4 = 8 = 1.6 kg. 5 5 Iron = 3 × 4 = 12 = 2.4 kg. 5 5
∴ Required ratio
= (1 + 1.6) : (2 + 2.4) = 2.6 : 4.4
= 13 : 22
- 729 ml of a mixture contains milk and water in the ratio 7 : 2. How much more water is to be added to get a new mixture containing milk and water in the ratio 7 : 3 ?
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In 729 ml of mixture,
Milk = 7 × 729 = 567 ml 9 Water = 2 × 729 = 162 ml 9
Let x ml of water be mixed.∴ 567 = 7 162 + x 3
⇒ 162 × 7 + 7x = 567 × 3
⇒ 1134 + 7x = 1701
⇒ 7x = 1701 – 1134 = 567⇒ x = 567 = 81 ml. 7 Correct Option: A
In 729 ml of mixture,
Milk = 7 × 729 = 567 ml 9 Water = 2 × 729 = 162 ml 9
Let x ml of water be mixed.∴ 567 = 7 162 + x 3
⇒ 162 × 7 + 7x = 567 × 3
⇒ 1134 + 7x = 1701
⇒ 7x = 1701 – 1134 = 567⇒ x = 567 = 81 ml. 7
- A container contains 60 kg of milk. From this container 6 kg of milk was taken out and replaced by water. This process was repeated further two times. The amount of milk left in the container is
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Amount of milk left = Initial amount ×
1 − Amount taken out in each operation 
3 Initial amount = 60 1 − 6 3 60 = 60 1 − 6 3 10 = 60 × 9 × 9 × 9 10 10 10
= 43.74 kg.Correct Option: C
Amount of milk left = Initial amount ×
1 − Amount taken out in each operation 3 Initial amount = 60 1 − 6 3 60 = 60 1 − 6 3 10 = 60 × 9 × 9 × 9 10 10 10
= 43.74 kg.
- There are three containers of equal capacity. The ratio of Sulphuric acid to water in the first container is 3 : 2, that in the second container is 7 : 3 and in the third container it is 11 : 4. If all the liquids are mixed together, then the ratio of Sulphuric acid to water in the mixture will be :
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In the new vessel, we have.
Sulphuric acid = 3 + 7 + 11 5 10 15 = 18 + 21 + 22 = 61 30 30 Water = 2 + 3 + 4 5 10 15 = 12 + 9 + 8 = 29 30 30
∴ Sulphuric acid : Water= 61 : 29 30 30
= 61 : 29Correct Option: A
In the new vessel, we have.
Sulphuric acid = 3 + 7 + 11 5 10 15 = 18 + 21 + 22 = 61 30 30 Water = 2 + 3 + 4 5 10 15 = 12 + 9 + 8 = 29 30 30
∴ Sulphuric acid : Water= 61 : 29 30 30
= 61 : 29
