A vessel is filled with liquid, 2 parts of which are water and 3 parts syrup. How much of the mixture must be drawn off and replaced with water so that the new mixture has the ratio of water to syrup in1:1?
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Solution
Suppose the vessel initially contains 5 litres of liquid.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture = litres
Quantity of syrup in new mixture = litres
=
⇒ 6x = 5
⇒ x = 5/6
So, part of the mixture replaced = (5/6) × (1/5) = 1/6 part
A man covered a distance of 2000 km in 18 hours partly by bus at72 kmph and partly by train at 160 kmph. The distance covered by bus is
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Solution
Average Speed = km/hr
By rule of alligation
Slower Speed Faster Speed
ratio of time = 5 : 4
Distance traveled by bus =
= 720 km
A container contains 60 litres of milk. From this container 6 litres of milk was taken out and replaced by water. This process was repeated further one more time. How much milk is now contained by the container?
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Solution
Amount of milk left after 2 operations
litres = = 48.60 litres.
A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. What is the percentage of water in the mixture?
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Solution
Let C.P. of 1 litre milk be Re. 1.
Then, S.P. of 1 litre of mixture = Re. 1. Gain = 25%.
C.P. of 1 litre mixture = Re.
C.P. of 1 litre milk C.P. of 1 litre of water
∴ Ratio of milk to water = = 4 : 1
Hence, percentage of water in the mixture = % = 20%
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:
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Solution
By the rule of allegation, we have:
Strength of first jar Strength of 2nd jar
So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2.
∴ Required quantity replaced = .
400 gm sprit solution has 40% spirit in it, How may grams of spirit should be added to make it 60% in the solution?
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Solution
By applying rule of allegations and mixtures
∴ Required ratio 2 : 1
Required amount of sprite = × 400 = 200 gm
In the 75 litres of mixture of milk and water, the ratio of milk and water is 4:1. Find the quantity of water required to be added to make the ratio of milk and water 3:1 in new mixture.
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Solution
Total quantity of mixture = 75 litre
Let x is quantity of water added to mixture (in litre).
Milk : Water = 4 : 1
Required ratio = 3 : 1
× (75) = × (75 + x)
Solving, we get x = 5 litre
An 10 kg alloy consist copper and zinc in the ratio of 3 : 2, in what quantity zinc should be mixed with it so that ratio in new mixture becomes 1 : 1 ?
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Solution
Since quantity of copper is unchanged.
Let quantity of zinc added is x kg.
So, 3 over 5 × 10 = 1 half (10 + x)
⇒ 6 = 5 + straight x over 2
⇒ x = 2 kg.
In 45 litres of mixture the ratio of water to alcohol is 3 : 7. Then find the difference between quantities of alcohol and water in the mixture?
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Solution
The required difference ⇒ × 45 = 18 litres
The respective ratio of milk and water in the mixture is 4 : 3. When 6 litres of water is added the ratio becomes 8 : 7. What is the quantity of milk in original mixture?
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Solution
Since quantity of milk is unchanged.
Let quantity of mixture ⇒ x L.
So, × x = × (x + 6)
⇒
⇒ x = = 84 L.
Quantity of milk = × 84 = 48 L.