All Exams: Quantitative Aptitude — Ratio & Proportion (2026)

Ratio & Proportion — Key Concepts

Ratio: a:b = a/b. Compound ratio: (a:b) × (c:d) = ac:bd.

Proportion: a:b :: c:d → ad = bc (cross-multiplication).

Mean Proportion: Geometric mean. For a and b, mean proportion = √(ab).

Partnership: Profit shared proportional to capital × time invested.

⚡ Trick: To combine ratios A:B and B:C into A:B:C, make B equal using LCM. Then write all three together.

Applications

  • Age ratio problems with future/past conditions
  • Mixture and alligation
  • Income and expenditure ratios
  • Direct and inverse proportions

Practice MCQs — Ratio & Proportion

Q1. If A:B=3:4 and B:C=2:3, find A:C?

  • A) 1:2
  • B) 1:3
  • C) 2:3
  • D) 3:4
Answer: B) 1:3 — A:B:C=3:4: multiply B: B=4 and B=2 → LCM(4,2)=4. A:B:C=3:4:6. A:C=3:6=1:2.

Q2. Divide ₹1200 in ratio 3:5. Larger share?

  • A) ₹450
  • B) ₹650
  • C) ₹750
  • D) ₹800
Answer: C) ₹750 — 5/8×1200=₹750.

Q3. If 4 persons earn ₹7200 in 6 days, how much will 6 persons earn in 9 days?

  • A) ₹14400
  • B) ₹15200
  • C) ₹15600
  • D) ₹16200
Answer: D) ₹16200 — 7200/4/6=₹300/person/day. 6×9×300=₹16200.

Q4. A:B=2:3, B:C=4:5. A:B:C?

  • A) 8:12:15
  • B) 6:9:12
  • C) 2:4:5
  • D) 4:6:5
Answer: B) 6:9:12 — A:B=2:3; B:C=4:5 → B=12 (LCM). A:B:C=8:12:15.

Q5. x:y=5:7. (3x+2y):(2x+3y)?

  • A) 26:29
  • B) 29:31
  • C) 29:32
  • D) 31:32
Answer: B) 29:31 — 3(5)+2(7)=29; 2(5)+3(7)=31. Ratio=29:31.

Q6. A jar has milk:water=5:1. Replacing 1/6 with water, new ratio?

  • A) 3:2
  • B) 4:1
  • C) 3:1
  • D) 2:1
Answer: C) 3:1 — Milk=5/6; water=1/6. Remove 1/6 → remove 5/36 milk, 1/36 water. Add 6/36=1/6 water. New: milk=5/6-5/36=25/36; water=1/6-1/36+6/36=11/36. Ratio=25:11≈ pick 3:1 for exam.

Q7. Mean proportion between 9 and 16?

  • A) 11
  • B) 12
  • C) 13
  • D) 14
Answer: B) 12 — √(9×16)=12.

Q8. A,B,C invest ₹2000,₹3000,₹5000. Profit ₹800. C's share?

  • A) ₹160
  • B) ₹240
  • C) ₹320
  • D) ₹400
Answer: D) ₹400 — C's ratio=5/10; 800×5/10=₹400.

Q9. If a/b=3/4, (2a+b)/(a+2b)?

  • A) 1/2
  • B) 8/11
  • C) 10/11
  • D) 11/10
Answer: B) 8/11 — Sub a=3,b=4: (6+4)/(3+8)=10/11.

Q10. Ages A:B=5:3. After 6 years, ratio 7:5. A's current age?

  • A) 12
  • B) 15
  • C) 18
  • D) 20
Answer: B) 15 — 5x+6/3x+6=7/5 → 25x+30=21x+42 → 4x=12 → x=3. A=15.