Ratio & Proportion
Ratio & Proportion
Ratio compares two quantities; proportion equates two ratios. SSC CGL, RRB NTPC, and IBPS Clerk test ratio in almost every paper, often embedded inside age, partnership, and mixture problems. Always reduce a ratio to lowest terms before solving. Cross-multiplication resolves any proportion with one unknown in a single step.
Key Idea
A ratio gives relative size, not absolute size. Always reduce to lowest terms (divide by GCD) before working with a ratio.
Core Formulas
Proportion (Cross-multiplication)
a:b :: c:d → a × d = b × c
Cross-multiply to find the missing term when the problem gives three of four values in a proportion.
Divide quantity in ratio a:b
First part = Total × a/(a+b); Second = Total × b/(a+b)
Split any total (money, weight, mixture) into parts \u2014 divide each part\u2019s ratio share by the sum of ratio terms, then multiply by the total.
Compounded Ratio
a:b compounded with c:d = ac : bd
When two ratios need to be combined into a single ratio.
Mean Proportion
Mean proportion of a and b = √(ab)
When asked to find the mean proportional between two numbers.
Third Proportion
Third proportion of a and b = b² / a
When asked to find x such that a:b :: b:x.
Relevant Exams
Ratio & Proportion underlies age problems, partnership, and mixture questions — all high-frequency topics in SSC CGL, RRB NTPC, and IBPS Clerk exams.