Ratio and Proportion Tricks for SSC CGL with Solved Examples

Quick answer: Ratio is the base of mixtures, partnership, ages and DI. Learn these six tricks and most questions take 20 seconds.

Tricks

• Combine ratios: A : B = 2 : 3, B : C = 4 : 5 → A : B : C = 8 : 12 : 15 (make B equal).
• Proportion: a : b :: c : d → ad = bc; mean proportional of a and c = √(ac); third proportional to a, b = b²/a.
• Componendo–dividendo: if a/b = c/d then (a + b)/(a − b) = (c + d)/(c − d).
• Partnership: profit ∝ capital × time.
• Alligation: (cheaper quantity)/(dearer quantity) = (dearer price − mean)/(mean − cheaper price).
• Ages: difference in ages never changes; use it as the anchor.

Solved questions

1. Divide ₹1200 in ratio 2 : 3 : 5 → 240, 360, 600
2. A : B = 3 : 4, B : C = 5 : 6 → A : B : C = 15 : 20 : 24
3. Ratio 3 : 5 becomes 5 : 7 when 4 is added to each → numbers 6 and 10
4. Mean proportional of 4 and 9 = 6
5. Third proportional to 6 and 12 = 24
6. A invests ₹5000 for 12 months, B ₹6000 for 8 months → profit ratio 60 : 48 = 5 : 4
7. Rice at ₹30 and ₹40 mixed to get ₹36 → ratio 4 : 6 = 2 : 3
8. Milk : water = 5 : 1 in 36 L; add water to make it 5 : 3 → add 12 L
9. Ages ratio 4 : 5, after 6 years 5 : 6 → present ages 24, 30
10. If x : y = 3 : 4, (2x + 3y) : (3x + 2y) = 18 : 17
11. Salaries 2 : 3, each gets +₹500, new ratio 3 : 4 → original 1000, 1500
12. Two numbers in 5 : 7, HCF 4 → numbers 20, 28
13. A vessel has 60 L milk; 6 L removed and replaced with water twice → milk = 60 × (0.9)² = 48.6 L
14. Incomes 3 : 4, expenses 2 : 3, each saves 1000 → incomes 3000, 4000
15. Coins of 1, 2, 5 in ratio 3 : 2 : 1 total ₹120 → 30, 20, 10 coins

Replacement formula

Final quantity = initial × (1 − removed/total)ⁿ.

Common mistakes

• Adding the ratio parts without a common middle term
• Using time-unaware partnership ratios
• Forgetting the age difference stays constant

Related: SI and CI tricks.

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Frequently asked questions

Which exams is this Ratio and Proportion Tricks guide useful for?

SSC CGL, CHSL, MTS, GD, RRB NTPC and Group D, IBPS and SBI PO/Clerk, state PSC and other exams with a similar syllabus.

How much practice is needed for Ratio and Proportion Tricks?

Solve 20–30 questions daily for one to two weeks with a timer. Track the time per question and your accuracy; move on once accuracy is above 90 percent.

Can I get ratio and proportion questions explained in Hindi?

Yes. DoubtPay AI explains any question in Hindi, Hinglish, English and nine other Indian languages, with step-by-step working. Packs start at ₹9 for 15 answers.