Ratio and Proportion | General Aptitude for GATE PSU ESE AE/JE

Ratio and Proportion is a fundamental topic in General Aptitude and is widely used in exams like GATE, PSU, ESE, AE/JE. It forms the base for many other topics like percentages, mixtures, and time & work.

What is Ratio?

A ratio is a comparison of two quantities of the same kind using division.

Formula:
Ratio = a : b = a / b

Example:

If A has 20 apples and B has 10 apples:
Ratio (A : B) = 20 : 10 = 2 : 1

What is Proportion?

Proportion means equality of two ratios.

Formula:
a : b = c : d ⇒ (a/b) = (c/d)

Cross Multiplication:
a × d = b × c

Important Concepts

• Direct Proportion: Increase in one leads to increase in another
• Inverse Proportion: Increase in one leads to decrease in another
• Continued Proportion: a : b = b : c

Important Formulas & Tricks

• If a : b = m : n, then a = km and b = kn
• Sum of ratios = Total quantity
• For three variables: a : b : c
• Convert ratios into fractions for faster calculation

Questions

Question 1

Divide ₹600 in the ratio 2 : 3.

Solution:
Total ratio = 2 + 3 = 5
First part = (2/5) × 600 = ₹240
Second part = (3/5) × 600 = ₹360
Answer: ₹240 and ₹360

Question 2

If a : b = 3 : 4 and b : c = 2 : 5, find a : b : c.

Solution:
Make b same:
a : b = 3 : 4 = 6 : 8
b : c = 2 : 5 = 8 : 20
Therefore, a : b : c = 6 : 8 : 20 = 3 : 4 : 10
Answer: 3 : 4 : 10

Question 3

If two numbers are in the ratio 5 : 7 and their sum is 96, find the numbers.

Solution:
Total ratio = 5 + 7 = 12
First number = (5/12) × 96 = 40
Second number = (7/12) × 96 = 56
Answer: 40 and 56

Common Mistakes to Avoid

• Not simplifying ratios properly
• Ignoring common factors
• Errors in cross multiplication

Exam Tips

• Convert ratios into fractions for quick solving
• Practice mixed questions regularly
• Focus on concept clarity

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