QUANT SHORTCUT | 23 OCTOBER 2026
Two ratios are given: A : B = 4 : 5 and B : C = 3 : 7. Find A : B : C. The answer is 12 : 15 : 35, and Amit Sir gets it in two quick multiplications, with no fractions and no LCM table. The whole trick rests on one observation: B appears in both ratios, so make B the same number in both. This page explains why that works, walks through his method step by step, shows a faster LCM version, and gives you worked examples and 10 practice questions.
The trap: just joining the numbers
The quick guess is to write the two ratios side by side and read off 4 : 5 : 7. Check it: that would make B : C = 5 : 7, but the question says B : C = 3 : 7. The guess fails because the “5” in the first ratio and the “3” in the second ratio are both B, measured in different units. A ratio only tells you proportions, so before two ratios can be joined, the shared term has to be written in the same units.
The key idea: make the common term equal
Multiplying both terms of a ratio by the same number does not change it: 4 : 5 is the same as 8 : 10 or 12 : 15. So you are free to scale each ratio until B has the same value in both. Once B matches, the two ratios are describing the same B, and you can read A, B and C off one line. This works for any chain of ratios that share a term, such as salaries of three people, ages, or the parts of a mixture.
Amit Sir’s method, step by step
- Spot the common term: B is in both ratios. In A : B = 4 : 5, B is 5. In B : C = 3 : 7, B is 3.
- Multiply each ratio by the other ratio’s B: multiply A : B by 3 and B : C by 5. You get 12 : 15 and 15 : 35.
- Check that B now matches: B is 15 in both, so the two ratios now use the same units.
- Read the answer: A : B : C = 12 : 15 : 35. The three numbers share no common factor, so this is already in lowest terms.
The faster LCM version
Cross-multiplying always works, but it can give big numbers. If the two B values share a factor, scale to their LCM instead. For A : B = 7 : 9 and B : C = 3 : 4, the B values are 9 and 3, and their LCM is 9. Leave the first ratio as it is and multiply the second by 3: 3 : 4 becomes 9 : 12, so A : B : C = 7 : 9 : 12. Cross-multiplying would have given 21 : 27 : 36, which reduces to the same answer.
Check the answer in two seconds
Take the answer apart again. From 12 : 15 : 35, A : B = 12 : 15 = 4 : 5 and B : C = 15 : 35 = 3 : 7. Both match the question, so the answer is right. This check catches almost every slip, including the 4 : 5 : 7 guess, where B : C comes out as 5 : 7.
More worked examples
- Simple chain: A : B = 3 : 2 and B : C = 5 : 4. Multiply by 5 and 2: 15 : 10 and 10 : 8, so A : B : C = 15 : 10 : 8.
- LCM shortcut: A : B = 7 : 9 and B : C = 3 : 4. Scale only the second ratio by 3: A : B : C = 7 : 9 : 12.
- Sharing an amount: ₹620 is shared among A, B and C in the ratio 12 : 15 : 35. The parts add to 62, so one part is ₹10 and the shares are ₹120, ₹150 and ₹350.
To join A : B and B : C, multiply each ratio by the other ratio’s B (or scale both to the LCM of the two B values); when B matches, read A : B : C straight off and reduce if the three numbers share a factor.
- Quantitative Techniques sets often give two or three linked ratios (salaries, investments, ages) and then ask for one share.
- Once you have A : B : C, a total turns into shares with one division: total ÷ sum of the parts = one part.
- For four terms (A : B, B : C, C : D), repeat the step: join the first two, then match C with the third ratio.
- Always check the joined ratio against both given ratios before you mark it.
| Fact | Detail |
|---|---|
| Question | A : B = 4 : 5, B : C = 3 : 7, find A : B : C |
| Common term | B (5 in the first ratio, 3 in the second) |
| Multiply | A : B × 3 = 12 : 15; B : C × 5 = 15 : 35 |
| B matches | 15 in both |
| Answer | A : B : C = 12 : 15 : 35 |
| Check | 12 : 15 = 4 : 5 and 15 : 35 = 3 : 7 |
| Wrong answer to avoid | 4 : 5 : 7 (it makes B : C = 5 : 7) |
The letter in both ratios must carry the same number. Multiply each ratio by the other one’s B, and the chain joins itself.
Sources
Amit Sir’s CLAT Gurukul class recording (the 2-Second Trick series, episode 7); the method is standard ratio arithmetic.
Free in the CLAT Gurukul app
These notes (as a PDF lesson) and the 10-question CBT are in the app under Current Affairs → 23 Oct 2026. Get the app on Google Play or open app.clatgurukul.com.
Practice Quiz — 10 CLAT-Style Questions
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