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Eduqo

Quantitative Aptitude›Ch 1: Arithmetic Foundations›Ratio and Proportion Masterclass

1.7

Ratio and Proportion Masterclass

5 min

Master foundational concepts, proportions, and division rules for competitive exams.

Golden Rule of Ratio

A ratio compares two quantities of the same unit through division. To preserve proportionality, always multiply or divide both terms by the same non-zero number.

Why This Topic Matters

Forms the bedrock of arithmetic topics like partnership and mixture.
Directly tested in SSC, Railway, and Defence quantitative sections.
Saves precious calculation time when solving complex word problems.

Quick Memory Hooks

Mean Proportional: b = sqrt(a * c)
Third Proportional: c = (b^2) / a
Compound Ratio: Multiply respective antecedents and consequents.

Proportion Types Cheat Sheet

Proportion Type	Given Terms	Formula / Rule
Fourth Proportional	a, b, c	d = (b * c) / a
Mean Proportional	a, b	x = sqrt(a * b)
Third Proportional	a, b	c = (b^2) / a

Visualizing Proportions

Compound

(Multiply ratios)

Multiply ratios

Compound 2:3 and 4:5 to get 8:15.

Division

(Share amount)

Share amount

Divide Rs 70 in 3:4 ratio as Rs 30 and Rs 40.

Mean Prop

(Geometric mean)

Geometric mean

Mean proportional of 4 and 9 is 6.

Proportion

(Equal ratios)

Equal ratios

If a:b = c:d, then ad = bc.

Exam Traps & Pitfalls

Adding same number to termsMultiply terms by variables

Never add a fixed number to ratio terms directly; always use a common multiplier variable like x.

Confusing third & mean propCheck formulas separately

Third proportional uses two terms as (b^2)/a, while mean proportional uses sqrt(ab). Do not mix them up.

Comparing different unitsConvert units to be equal

Always convert rupees to paise or meters to centimeters before taking a ratio.

Test Your Skills

Q1.Find the mean proportional between 9 and 25.

Q2.If Rs 560 is divided among A, B, and C in the ratio 1/2 : 1/3 : 1/4, what is B's share?

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