🧠 Ratio, Proportion, and Percentage

Summary Cheat Sheet

• Ratio compares like quantities; proportion sets two ratios equal.
• Percentage expresses part per hundred and supports growth/decline analysis.
• Farm applications include nutrient composition, germination, moisture, and interest.

References

1 source

This lesson covers ratio, proportion, and percentage methods that support fertilizer blending, yield comparison, and farm accounting.

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Ratio

A ratio compares two quantities of the same kind by division. The ratio of a to b is written as a:b or a/b. Ratios have no units and should be expressed in their simplest form by dividing both terms by their Greatest Common Divisor (GCD).

Example: If a farm has 120 mango trees and 80 guava trees, the ratio of mango to guava is 120:80 = 3:2 (dividing both by 40).

Types of ratios:

• Compound ratio: Ratio of products. If a:b = 2:3 and c:d = 4:5, compound ratio = (2x4):(3x5) = 8:15
• Duplicate ratio: The square of a ratio. Duplicate of 3:4 is 9:16
• Inverse ratio: Reciprocal. Inverse of 2:5 is 5:2

Proportion

A proportion states that two ratios are equal: a:b = c:d (read as "a is to b as c is to d"). Here, a and d are called extremes, and b and c are called means. The fundamental property is: a x d = b x c (product of extremes equals product of means).

Direct proportion: When one quantity increases, the other increases proportionally. Example: If 5 kg of seeds cost Rs. 200, how much do 12 kg cost? By proportion: 5/200 = 12/x, so x = (200 x 12)/5 = Rs. 480.

Inverse proportion: When one quantity increases, the other decreases. Example: If 8 workers can harvest a field in 6 days, how many days would 12 workers take? Workers x Days = constant, so 8 x 6 = 12 x d, giving d = 48/12 = 4 days.

Percentage

A percentage expresses a number as a fraction of 100 (per centum = per hundred). To convert a fraction to percentage: multiply by 100. To convert percentage to fraction: divide by 100.

Key formulas:

• Percentage = (Part / Whole) x 100
• Percentage increase = ((New - Old) / Old) x 100
• Percentage decrease = ((Old - New) / Old) x 100

Applications in Agriculture

Fertilizer mixtures: NPK fertilizers are labelled by percentage composition. A 10-26-26 fertilizer contains 10% nitrogen, 26% phosphorus, and 26% potassium. If a farmer needs 50 kg of phosphorus per hectare, the amount of this fertilizer required = 50 / 0.26 = 192.3 kg.

Yield calculations: If last year's wheat yield was 40 quintals/hectare and this year it is 46 quintals/hectare, the percentage increase = ((46 - 40)/40) x 100 = 15%.

Germination percentage: If out of 400 seeds tested, 340 germinate, the germination percentage = (340/400) x 100 = 85%. Seeds with germination below 75% are generally not recommended for sowing.

Moisture content: Grain moisture content is critical for storage. If 100 g of paddy loses 14 g of water on drying, moisture content = (14/100) x 100 = 14%. Safe storage typically requires moisture below 12-14%.

Loan interest: A farmer borrows Rs. 50,000 at 7% annual interest. Interest for one year = 50000 x 7/100 = Rs. 3,500. Compound interest calculations use the formula A = P(1 + r/100)^n, where P is the principal, r is the rate, and n is the number of years.

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