Alligation or Mixture Moderate Questions and Answers

Alligation or Mixture

A container is full of milk. One-third of milk is taken out of it and replaced by same quantity of water. Then again one-third of the mixture is taken out of it and replaced by the same quantity of water. The process is repeated 4 times. If 16 litres of milk is left in the container at the end of 4th operation, find the capacity of the container.

Let capacity of the container be P liter; then
P(1 – 1/3)4 = 16

Correct Option: B

Let capacity of the container be P liter; then
P(1 – 1/3)⁴ = 16
⇒ P (2 / 3)⁴ = 16
⇒ P(16 / 81) = 16 liters
∴ P = 81 liters

In a courtyard there are many chickens and goats. If heads are counted, it comes to 100 but when legs are counted, it comes to 320. Find the number of chickens and goats in the courtyard.

Average no. of legs per head = (320 / 100) = (16 / 5)

Correct Option: C

Average no. of legs per head = (320 / 100) = (16 / 5)
or, 3 : 2
No. of goats = (3 / 3 + 2) × 100 = 60
No. of chickens = 100 – 60 = 40.

If 4 kg of an alloy made of 1/4th iron and rest is mixed with 6 kg of another alloy made of 2/3rd iron and rest tin, find the ratio of iron to tin in the resultant mixture.

Total quantity of iron = 4 (1 / 4) + 6 (2 / 3) = 1 + 4 = 5 kg.

Correct Option: A

Total quantity of iron = 4 (1 / 4) + 6 (2 / 3) = 1 + 4 = 5 kg.
Total quantity of tin = (4 + 6) – 5 = 5 kg.
In the resultant mixture, iron : tin = 5 : 5 or 1 : 1

The average monthly salary of employees, consisting of officers and workers, of an organisation is Rs. 3000. The average salary of an officer is Rs. 10,000 while that of a worker is Rs. 2000 per month. If there are total 400 employees in the organisation, find the number of officers and workers separately.

As per figure we can calculate the ration as below.
Number of officers / Number of workers = 1000 / 7000 = 1 / 7

Correct Option: B

As per figure we can calculate the ration as below
Number of officers / Number of workers = 1000 / 7000 = 1 / 7
No. of officers = 1 / (1 + 7) × 400 = 50
No. of workers = 400 – 50 = 350

A shopkeeper has 50 kgs of rice. He sells a part of it at 20% profit and the rest at 40% profit. If he gains 25% on the whole, find the quantity of each part.

According to figure we find that the ratio will be 3 : 1.

Correct Option: B

According to figure we find that the ratio will be 3 : 1.

Quantity sold at 20% profit = 3 / (3 + 1) × 50 = 37.5 kgs.
Quantity sold at 40% profit = (50 – 37.5) = 12.5 kgs.