Ratio and Proportion
About 7 min · Elementary Mathematics · English
Time worked out from the lesson's 459 words at 150 words a minute, plus a minute for each question.
Ratio and Proportion is a core topic in SSC GD Elementary Mathematics. Candidates often lose marks here not because the concepts are difficult, but because they rush through ratio simplification or skip unit checks.
Key ideas
- Ratio is the comparison of two quantities of the same kind, written as a:b or a/b. A ratio of 3:5 means the first quantity is 3 parts and the second is 5 parts out of a total of 8 parts.
- Proportion states that two ratios are equal: a:b = c:d or a/b = c/d. The cross-multiplication property ad = bc is the workhorse for solving proportion problems.
- Compound ratio is the ratio obtained by multiplying the numerators and denominators of two or more ratios. The compound ratio of a:b and c:d is (ac):(bd).
- Continued ratio a:b:c means a quantity is divided into parts in the ratio a, b, and c. If the total is T, then the three parts are (a/(a+b+c))×T, (b/(a+b+c))×T, and (c/(a+b+c))×T.
- Fourth proportional to a, b, c is d such that a:b = c:d. Solve for d = (b×c)/a.
Watch out for
- Forgetting to add denominators: When dividing a sum in ratio a:b, students often compute a/b × sum instead of a/(a+b) × sum. Always add the ratio terms first to find total parts.
- Mixing up time and investment in partnership: If two partners invest for different durations, profit depends on (Investment × Time), not just Investment. Read the question carefully—equal time means ignore time; different times means multiply each investment by its time.
- Cross-multiplication errors: In a:b = c:d, the correct equation is ad = bc, not ac = bd. Write it out explicitly to avoid flipping terms.
Quick reference
- Ratio a:b means first part is (a/(a+b)) of the total, second part is (b/(a+b)) of the total.
- Proportion: a:b = c:d ⇒ ad = bc. Use cross-multiplication to solve for the unknown term.
- Compound ratio of a:b and c:d is (ac):(bd).
- Partnership (equal time): Profit ratio = Investment ratio.
- Partnership (unequal time): Profit ratio = (Investment × Time) ratio.
Check yourself: 3 questions
1. Two numbers are in the ratio 3 : 5. If 9 is added to each number, the ratio becomes 12 : 17. What is the smaller number?
2. A, B and C start a business with investments in the ratio 2 : 3 : 5. After one year, their profits are in the ratio 4 : 3 : 5. If A invested for 12 months, for how many months did B invest?
3. If A : B = 2 : 3 and B : C = 4 : 5, then what is A : B : C?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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