ICO Direct Proportion Calculator – Definition, Formula & Solved Examples

Understanding direct proportion is one of the most important concepts in basic mathematics. It helps students solve real-life problems related to cost, distance, wages, height, fuel consumption, and many other daily situations.

Direct Proportion Calculator (Step-by-Step)

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In this detailed guide, we will explain the concept of direct proportion سڌي تناسب, its formula, and provide five fully solved examples of proportion with step-by-step solutions.

What is Direct Proportion سڌي تناسب?

Two quantities are said directly proportion when an increase in one quantity causes a proportional increase in the other quantity. Similarly, when one decreases, the other decreases in the same ratio.

Simple Definition:If:

[ \frac{a}{b} = \frac{c}{d} ]

Then the quantities are in direct proportional

In simple words:

When one value increases, the other also increases in the same ratio.

Formula of Direct Proportion: If two quantities are directly proportional:

[ a \propto b ]

Or,

[ \frac{a}{b} = constant ]

To solve problems, we use cross multiplication:

[ a \times d = b \times c ]

✅ Example 1: Height and Shadow (Direct Proportion)

If a man of height 150 cm casts a shadow of 100 cm,
what will be the shadow of a man whose height is 180 cm?

Step 1: Set up the proportion

[ \frac{150}{100} = \frac{180}{x} ]

Step 2: Cross multiply

[ 150x = 18000 ]

Step 3: Solve

[ x = \frac{18000}{150} ]

[ x = 120 ]

Final Answer:

The shadow is 120 cm.

Since height increases, shadow length also increases.
This confirms direct proportional

✅ Example 2: Cost and Quantity

If 5 books cost Rs. 750,
how much will 8 books cost?

Step 1:

[ \frac{5}{750} = \frac{8}{x} ]

Step 2: Cross multiply

[ 5x = 6000 ]

Step 3:

[ x = \frac{6000}{5} ]

[ x = 1200 ]

Final Answer:

8 books cost Rs. 1200.

As the number of books increases, cost increases.
This is a classic example of direct proportion.

✅ Example 3: Wages and Days Worked

If a worker earns Rs. 2000 in 4 days,
how much will he earn in 7 days?

Step 1:

[ \frac{4}{2000} = \frac{7}{x} ]

Step 2:

[ 4x = 14000 ]

Step 3:

[ x = \frac{14000}{4} ]

[ x = 3500 ]

Final Answer:

He earns Rs. 3500 in 7 days.

More days worked → more wages earned.
This shows direct proportionality

✅ Example 4: Distance and Fuel

If a car travels 120 km using 10 liters of fuel,
how far will it travel using 15 liters?

Step 1:

[ \frac{120}{10} = \frac{x}{15} ]

Step 2:

[ 10x = 1800 ]

Step 3:

[ x = \frac{1800}{10} ]

[ x = 180 ]

Final Answer:

The car will travel 180 km.

More fuel → more distance traveled.
Again, this is proportional but direct

✅ Example 5: Students and Notebooks

If 6 students need 18 notebooks,
how many notebooks will 10 students need?

Step 1:

[ \frac{6}{18} = \frac{10}{x} ]

Step 2:

[ 6x = 180 ]

Step 3:

[ x = \frac{180}{6} ]

[ x = 30 ]

Final Answer:

10 students need 30 notebooks.

More students → more notebooks required.(Directly proportionL)

Key Characteristics

✔ Both quantities increase together
✔ Both quantities decrease together
✔ Ratio between them remains constant
✔ Graph of direct proportion is a straight line passing through origin

Real-Life Importance of Direct Proportion

This concept of is widely used in:

Shopping and pricing
Salary calculations
Fuel consumption
Construction material estimation
Business profit calculation
School mathematics

Understanding it makes it easier to solve practical and academic problems quickly.

Conclusion

The concept of direct proportion is simple yet powerful. Whenever two quantities increase or decrease together in the same ratio, they are directly proportional.By using cross multiplication and setting up proper ratios, students can easily solve proportion problems.