# Alligation & Mixtures Model Questions Set 1 Practice Questions Answers Test With Solutions & More Shortcuts

#### ALLIGATION & MIXTURES PRACTICE TEST [1 - EXERCISES]

Question : 1

A vessel of 80 litre is filled with milk and water. 70% of milk and 30% of water is taken out of the vessel. It is found that the vessel is vacated by 55%. Find the initial quantity of milk and water.

a) 30, 50

b) 60, 20

c) 20, 60

d) 50, 30

e) None of these

Here, the % values of milk and water that is taken from the vessel should be taken into consideration.

⇒5 : 3

Ratio of milk to water = 5 : 3

∴ quantity of milk = \${80}/{5 + 3}\$ × 5 = 50 litres

and quantity of milk = \${80}/{5 + 3}\$ × 3 = 30 litres

Question : 2

Gold is 19 times as heavy as water and copper 9 times. In what ratio should these metals be mixed so that the mixture may be 15 times as heavy as water?

a) 3 : 2

b) 4 : 5

c) 1 : 2

d) 2 : 3

e) None of these

∴ Gold : Copper = 6 : 4 = 3 : 2

Question : 3

In what ratio must water be mixed with milk costing Rs. 12 per litre to obtain a mixture worth of Rs. 8 per litre?

a) 2 : 1

b) 3 : 2

c) 1 : 2

d) 2 : 3

e) None of these

By the rule of alligation:

Ratio of water to milk = 4 : 8 = 1 : 2

Question : 4

Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.

a) 2 : 3

b) 4 : 5

c) 1 : 3

d) 3 : 4

e) None of these

By the rule of alligation:

∴ Required rate = 60 : 90 = 2 : 3

Question : 5

A container contained 80 kg of milk. From this container, 8 kg of milk was taken out and replaced by water. This process was further repeated two times. How much milk is now contained by the container?

a) 56 kg

b) 59.46 kg

c) 48 kg

d) 58.32 kg

e) None of these

Amount of liquid left after n operations, when the container

originally contains x units of liquid from which y units in

taken out each time is x \$({x - y}/x)^n\$ units.

Thus, in the above case, amount of milk left

= 80\$[{80 - 8}/80]^3\$ kg = 58.32 kg

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