Unitary Method
The Unitary Method is one of the most important arithmetic techniques used in CMAT, KUUMAT, BBA, BIM, BHM, and management entrance examinations. It involves finding the value of one unit first and then calculating the required value.
Practice MCQs for Unitary Method
Fundamental Principles
Unitary Method
A method of solving problems by first finding the value of one unit and then finding the value of the required number of units.
Direct Variation
When one quantity increases or decreases in the same proportion as another quantity.
Inverse Variation
When one quantity increases while the other decreases proportionally.
Rate
A comparison of two quantities having different units.
Efficiency
The amount of work completed per unit time.
Essential Formulation Tips
- Read the problem carefully before deciding whether it is direct or inverse variation.
- Write all quantities with units.
- Convert all measurements into the same unit when necessary.
- Use tables to organize information.
- Check whether the answer is reasonable.
Shortcut Execution Techniques
- If quantity increases and result increases, use direct proportion.
- If quantity increases and result decreases, use inverse proportion.
- For workers and days, think inverse proportion.
- For cost and quantity, think direct proportion.
- For speed and time covering the same distance, think inverse proportion.
Contextual Inquiries (FAQs)
Q: What is the first step in the unitary method?
A: Find the value of one unit.
Q: How do I know whether to use direct or inverse proportion?
A: If both quantities move in the same direction, use direct proportion. If one increases while the other decreases, use inverse proportion.
Q: Why is the unitary method important for CMAT?
A: It is widely used in arithmetic, work, distance, ratio, and business mathematics problems.
Example Breakdown: Cost and Quantity
Basic unitary method.Cost of 1 notebook = 250 ÷ 5 = Rs. 50
Cost of 8 notebooks = 50 × 8 = Rs. 400
Example Breakdown: Workers and Days
Inverse proportion problem.Workers and days are inversely proportional.
10 × 12 = 15 × x
120 = 15x
x = 8 days
Example Breakdown: Distance and Speed
Direct proportion application.Speed = 240 ÷ 4 = 60 km/h
Distance in 7 hours = 60 × 7 = 420 km
Example Breakdown: Production Problem
Direct variation.Production per hour = 120 ÷ 3 = 40
Production in 8 hours = 40 × 8 = 320
Example Breakdown: Painting Work
CMAT-type work problem.Painters and days are inversely proportional.
6 × 15 = x × 9
x = 10 painters
CMAT Unitary Method Basics Set 1
Fundamental unitary method questions based on direct calculation.
Q1. If 5 pens cost Rs. 50, what is the cost of 1 pen?
Q2. If 3 kg rice costs Rs. 90, cost of 1 kg is:
Q3. If 10 notebooks cost Rs. 200, cost of 1 notebook is:
Q4. If 4 kg sugar costs Rs. 120, 1 kg costs:
Q5. If 6 oranges cost Rs. 90, cost of 1 orange is:
Q6. If 8 meters cloth costs Rs. 400, 1 meter costs:
Q7. If 12 eggs cost Rs. 96, cost of 1 egg is:
Q8. If 15 kg apples cost Rs. 600, 1 kg costs:
Q9. If 2 liters milk cost Rs. 110, 1 liter costs:
Q10. Unitary method is mainly used to find: