Ratio, Proportion
- The milk and water in a mixture are in the ratio 7 : 5. When 15 litres of water are added to it, the ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is
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Let the quantity of milk in the
mixture = 7x litres and that of
water = 5x litres.
According to the question,7x = 7 5x + 15 8
⇒ 56x = 35x + 105
⇒ 56 x – 35 x = 105
⇒ 21x = 105⇒ x = 105 = 5 21
∴ Required quantity of water
= (5x + 15) litres
= 5 × 5 + 15 = 40 litresCorrect Option: B
Let the quantity of milk in the
mixture = 7x litres and that of
water = 5x litres.
According to the question,7x = 7 5x + 15 8
⇒ 56x = 35x + 105
⇒ 56 x – 35 x = 105
⇒ 21x = 105⇒ x = 105 = 5 21
∴ Required quantity of water
= (5x + 15) litres
= 5 × 5 + 15 = 40 litres
- Vessels A and B contain mixtures of milk and water in the ratios 4 : 5 and 5 : 1 respectively. In what ratio should quantities of mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5 : 4?
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First of all we write the fraction of milk present in three mixtures.
In A; 4 and In B; 5 9 6 In combination of A and B; 5 9
From alligation rule,= 5 : 1 18 9 ⇒ 5 : 2 ⇒ 5 : 2 18 18
So, ratio of
A : B = 5 : 2Correct Option: C
First of all we write the fraction of milk present in three mixtures.
In A; 4 and In B; 5 9 6 In combination of A and B; 5 9
From alligation rule,= 5 : 1 18 9 ⇒ 5 : 2 ⇒ 5 : 2 18 18
So, ratio of
A : B = 5 : 2
- In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?
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Quantity of milk
= 7 × 80 = 56 litres 10
Quantity of water= 3 × 80 = 24 litres 10
Let x litre water be addedThen, 56 = 2 24 + x 1
⇒ 24 + x = 28
x = 4 litresCorrect Option: D
Quantity of milk
= 7 × 80 = 56 litres 10
Quantity of water= 3 × 80 = 24 litres 10
Let x litre water be addedThen, 56 = 2 24 + x 1
⇒ 24 + x = 28
x = 4 litres
- There is 81 litres pure milk in a container. One-third of milk is replaced by water in the container. Again one-third of mixture is extracted and equal amount of water is added. What is the ratio of milk to water in the new mixture?
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Quantity of milk in the last
= 81 1 − 27 2 = 81 1 − 1 2 81 3 = 81 × 2 × 2 = 36 3 3
Quantity of water in the last
= 81 – 36 = 45∴ Ratio = 36 × 4 = 4 : 5 45 5 Correct Option: D
Quantity of milk in the last
= 81 1 − 27 2 = 81 1 − 1 2 81 3 = 81 × 2 × 2 = 36 3 3
Quantity of water in the last
= 81 – 36 = 45∴ Ratio = 36 × 4 = 4 : 5 45 5
- A barrel contains a mixture of wine and water in the ratio 3 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1 : 1 ?
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Let the barrel contain 4 litres of mixture.
∴ Wine = 3 litres
Water = 1 litre
Let x litre mixture is taken out.
∴ Wine in (4 – x) litres mixture= 3 (4 − x) 4
On adding x litres water, water in mixture= (4 − x) × 1 + x 4 = 1 − x + x 4 = 4 − x + 4x = 4 + 3x 4 4 ∴ 3 (4 − x) = 4 + 3x 4 4 ⇒ 3 − 3x = 1 + 3x 4 4 ⇒ 2 = 6x 4 ⇒ x = 2 × 4 = 4 6 3 ∴ Required answer = (4/3) = 1 4 3 Correct Option: B
Let the barrel contain 4 litres of mixture.
∴ Wine = 3 litres
Water = 1 litre
Let x litre mixture is taken out.
∴ Wine in (4 – x) litres mixture= 3 (4 − x) 4
On adding x litres water, water in mixture= (4 − x) × 1 + x 4 = 1 − x + x 4 = 4 − x + 4x = 4 + 3x 4 4 ∴ 3 (4 − x) = 4 + 3x 4 4 ⇒ 3 − 3x = 1 + 3x 4 4 ⇒ 2 = 6x 4 ⇒ x = 2 × 4 = 4 6 3 ∴ Required answer = (4/3) = 1 4 3