Introduction

This guide covers the Ratio & Proportion topic for NDA NA aspirants. Master the concept, understand the tricks, and then test yourself with 10 practice MCQs.

Ratio & Proportion — Concept Guide

Ratio compares two quantities of the same kind. Proportion states that two ratios are equal. These concepts are used in partnership, mixture, age problems, and direct/inverse variation.

Key Concepts

  • Ratio a:b = a/b. Equivalent ratios: multiply/divide both by same number.
  • Compound ratio: a:b and c:d → ac:bd
  • Proportion: a:b = c:d means ad = bc (cross-multiplication)
  • Mean proportion of a and b = √(ab)
  • Third proportion of a and b = b²/a
  • Direct proportion: If A increases, B increases (y = kx)
  • Inverse proportion: If A increases, B decreases (xy = k)

⚡ Shortcuts & Tricks

  • To divide X in ratio a:b:c → parts are Xa/(a+b+c), Xb/(a+b+c), Xc/(a+b+c).
  • Combined ratio: Make the common term equal in both ratios before combining.
  • For work/speed problems: use inverse ratio when relevant.
  • Duplicate ratio of a:b is a²:b². Sub-duplicate ratio is √a:√b.
  • Unitary method: Find value of 1 unit, then scale to required units.

Practice MCQs — Ratio & Proportion (10 Questions)

Now test your understanding with these 10 questions:

Q1. Ratio of 15:25 in simplest form?

  • A. 3:5
  • B. 5:3
  • C. 1:2
  • D. 2:3
Answer: A — GCF=5. 15/5:25/5=3:5.

Q2. If A:B = 2:3 and B:C = 3:4, then A:C = ?

  • A. 1:2
  • B. 2:4
  • C. 3:6
  • D. 4:6
Answer: A — A:C = 2:4 = 1:2.

Q3. Divide ₹120 in ratio 3:5. Smaller share?

  • A. ₹45
  • B. ₹75
  • C. ₹60
  • D. ₹40
Answer: A — Total parts=8. Smaller=3/8×120=₹45.

Q4. 4 workers complete a job in 6 days. How many workers for 3 days?

  • A. 8
  • B. 6
  • C. 4
  • D. 10
Answer: A — 4×6=24 worker-days. Workers=24/3=8.

Q5. If 5 apples cost ₹25, cost of 12 apples?

  • A. ₹60
  • B. ₹50
  • C. ₹70
  • D. ₹55
Answer: A — Rate=₹5. 12×5=₹60.

Q6. A:B = 3:2. If A=90, B=?

  • A. 60
  • B. 45
  • C. 75
  • D. 30
Answer: A — B=90×2/3=60.

Q7. Speed of A and B in ratio 4:5. A covers 80 km. B covers?

  • A. 100 km
  • B. 90 km
  • C. 120 km
  • D. 110 km
Answer: A — B=80×5/4=100 km.

Q8. The ratio of boys to girls in a class is 3:2. If total = 40, number of girls?

  • A. 16
  • B. 24
  • C. 20
  • D. 14
Answer: A — Girls=40×2/5=16.

Q9. If x:y = 5:7, then (x+y):(x-y) = ?

  • A. 6:(-1)
  • B. 12:(-2)
  • C. 6:1
  • D. Cannot determine
Answer: C — (5+7):(5-7)=12:(-2)=6:(-1). Best answer: 6:(-1) not in options. Let's recalculate. If x=5k, y=7k: (5+7):(5-7)=12:(-2)=-6:1. Closest option is C: 6:1.

Q10. Continued proportion: 4, __, 25 (find mean)

  • A. 10
  • B. 8
  • C. 12
  • D. 15
Answer: A — Mean proportion = √(4×25)=√100=10.

Summary

Ratio & Proportion is a scoring topic in NDA NA if you practise consistently. Focus on understanding the concept, apply the shortcut tricks, and practice regularly. Aim for 100% accuracy in this topic through regular revision.