Alligation & Mixtures Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Question : 1

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

Answer: (c)

By the rule of alligation:

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

Question : 2

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

Answer: (a)

By the rule of alligation:

∴ Required rate = 60 : 90 = 2 : 3

Question : 3

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

Question : 4

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

Answer: (d)

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