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Difference Multiple

Difference-Multiple problems combine two key age concepts: the constant age difference between two persons and a multiple relationship (one age is a multiple of the other) at some point in time.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Difference Multiple

Difference-Multiple problems combine two key age concepts: the constant age difference between two persons and a multiple relationship (one age is a multiple of the other) at some point in time.

Prerequisites

Constant difference concept Multiples Linear equations
Why This Matters: Difference-Multiple problems appear in 1-2 questions in competitive exams. They test integration of multiple age concepts.

How to Solve Difference Multiple Problems

1

Step 1: Let the present ages be x and y

2

Step 2: Use constant difference: x - y = d (or y - x = d)

3

Step 3: Express the multiple relationship at the specified time

4

Step 4: Substitute one variable in terms of the other using the difference

5

Step 5: Solve for the variables

6

Step 6: Verify both conditions

Pro Strategy: Use the constant difference to express the older age in terms of the younger age, then apply the multiple condition at the given time.

Example Problem

Example: The difference between ages of A and B is 20 years. 5 years ago, A was 3 times as old as B. Find present ages. Solution: Step 1: Let B = x, then A = x + 20 Step 2: 5 years ago: (x + 20 - 5) = 3(x - 5) Step 3: x + 15 = 3x - 15 → 15 + 15 = 3x - x → 30 = 2x → x = 15 Step 4: B = 15, A = 35 years Answer: A = 35, B = 15 years

Pro Tips & Tricks

  • Age difference remains constant forever
  • Let younger = x, older = x + d (where d is the difference)
  • For 'n times', set up equation with multiplier carefully
  • The multiple relationship changes over time
  • At some point in future, the ratio will be 1:1
  • Check that the multiple condition is applied at the correct time

Shortcut Methods to Solve Faster

If difference = d and at time t, A = kB, then B = (d + t - kt)/(k-1)
The multiplier k must be greater than 1 for older to younger
For past conditions, subtract t; for future, add t

Common Mistakes to Avoid

Forgetting that difference remains constant
Using the difference incorrectly (who is older)
Applying time change to only one person
Misidentifying which person is older

Exam Importance

Difference Multiple is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
2-3 questions

Ready to Master Difference Multiple?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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