How to Solve Unitary Method Word Problems Step by Step
The concept of unitary method plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Students use the unitary method in maths to solve questions related to ratios, proportions, costs, time and work, and speed. This approach makes calculations simpler and faster for a wide range of problems.
What Is Unitary Method?
The unitary method in maths is a technique used to find the value of a single unit from the value of multiple units (or vice versa). Once the value for one unit is found, you can calculate the value for any other number of units by simple multiplication. You’ll find this concept applied in areas such as cost calculation, ratio and proportion, and percentage problems.
Key Formula for Unitary Method
Here’s the standard formula:
If the value of n units = A,
then, value of 1 unit = A ÷ n;
value of m units = (A ÷ n) × m
Cross-Disciplinary Usage
The unitary method is not only useful in maths but also plays an important role in Physics, Computer Science, and daily logical reasoning. For example, it is used in speed-distance-time problems, collaborative work, or making sense of ratios in chemical mixtures. Students preparing for JEE or NEET often see its relevance in applied and data interpretation questions.
Step-by-Step Illustration
Let’s solve an example using the unitary method:
Suppose 8 markers cost ₹120. What is the cost of 5 markers?
1. Value of 8 markers = ₹1202. Find the cost of 1 marker: ₹120 ÷ 8 = ₹15
3. Cost of 5 markers: ₹15 × 5 = ₹75
So, 5 markers will cost ₹75.
Speed Trick or Quick Shortcut
Here’s a quick shortcut for the unitary method in common exam scenarios:
Time & Work Example: If A can finish a task in 6 days, and B can do the same in 4 days, how long will they take if working together?
1. Work done by A in 1 day: 1 ÷ 6 = 1/62. Work done by B in 1 day: 1 ÷ 4 = 1/4
3. Combined work per day: 1/6 + 1/4 = (2+3)/12 = 5/12
4. Total time together = 1 ÷ (5/12) = 12/5 = 2.4 days
Tricks like solving for ‘one unit’ streamlines many word problems and is encouraged in school and competitive exams. Vedantu’s sessions share more such methods to help boost your marks efficiently.
Try These Yourself
- 8 apples cost ₹200. What is the cost of 3 apples?
- If 2 pens cost ₹34, how many pens can you buy with ₹170?
- A machine fills 300 bottles in 5 hours. How many bottles in 8 hours?
- If a cyclist covers 60 km in 3 hours, what is his speed per hour?
Frequent Errors and Misunderstandings
- Forgetting to first calculate the value of a single unit before moving to the required units.
- Mixing up direct and inverse variation, especially in time & work or speed problems.
- Arithmetic errors like dividing incorrectly or confusing units.
Relation to Other Concepts
The idea of unitary method closely connects with ratios and proportions as well as percentage. Mastering this method helps you simplify more complex chapters related to financial maths, speed-time-distance, and collaborative work.
Classroom Tip
A simple way to remember the unitary method: “First find the value of one, then multiply for many.” Draw a table or chart, with knowns on the left and unknowns on the right, as teachers at Vedantu often suggest to make the process error-free.
Wrapping It All Up
We explored the unitary method—from its definition and formula to examples, common mistakes, and its connection to other maths ideas. With practice and the right approach, you’ll solve such word problems quickly and gain confidence in all related chapters. For more practice, check out the Simple Interest and Speed Formula on Vedantu.
FAQs on Unitary Method: Definition, Formula, and Solved Examples
1. What is the unitary method in Maths?
The unitary method in Maths is a technique to solve problems by first finding the value of one unit, then using this to calculate the value of any required number of units. It's a stepwise method useful for solving problems involving ratio, proportion, time and work, and other real-world scenarios.
2. How do you solve unitary method word problems?
Solving unitary method word problems involves these steps:
1. Identify the unit (e.g., one apple, one hour of work) and its corresponding value (e.g., cost, amount of work).
2. Find the value of one unit by dividing the total value by the total number of units.
3. Multiply the value of one unit by the desired number of units to find the required value.
3. What is the unitary method formula?
There isn't a single formula, but the process follows this logic:
Value of one unit = Total value / Total number of units
Value of 'x' units = Value of one unit × x
4. Where is the unitary method used in daily life?
The unitary method is used in various daily situations, such as:
• Calculating the cost of multiple items based on the price of one item.
• Determining the time taken to complete a task given the rate of work.
• Figuring out fuel consumption based on distance traveled.
• Converting units of measurement (e.g., kilometers to miles).
5. What is the difference between unitary and direct proportion?
While both involve relationships between quantities, they differ in approach. Unitary method focuses on finding the value of a single unit first. Direct proportion states that if one quantity increases, the other increases proportionally (and vice versa), without necessarily calculating a single unit value first. The unitary method *can* be used to solve problems involving direct proportion.
6. Can the unitary method be applied to percentages and discounts?
Yes, the unitary method is applicable to percentages and discounts. You can find the value of 1% of a quantity and then multiply to find any percentage or discount amount.
7. Why is finding one unit crucial in the unitary method?
Finding the value of one unit is crucial because it provides a base value. From this base, you can calculate the value of any number of units through simple multiplication, making calculations efficient and straightforward.
8. How does the unitary method help in data interpretation questions?
The unitary method aids in data interpretation by allowing you to extract meaningful information from given data. For example, if you have data showing the total cost for a bulk purchase, you can use the unitary method to find the cost per unit and then compare with other similar data.
9. Are there any calculators for the unitary method online?
While dedicated unitary method calculators are less common, general calculators can be used to perform the division and multiplication steps involved in the method.
10. How can mistakes occur in unitary method calculations—and how to avoid them?
Common mistakes include incorrect unit identification, errors in division or multiplication, and misinterpreting the problem statement. To avoid mistakes:
• Carefully identify the units and their values.
• Double-check your calculations.
• Ensure you understand the question fully before starting.
11. What are the two types of unitary methods?
The unitary method can be applied to problems involving either direct variation or inverse variation. In direct variation, an increase in one quantity leads to a proportional increase in the other. In inverse variation, an increase in one quantity leads to a proportional decrease in the other.
12. How is the unitary method related to ratio and proportion?
The unitary method is closely related to ratio and proportion. Many problems solvable by the unitary method also involve ratios and proportional relationships between quantities. The unitary method provides a systematic approach for solving these types of problems.
