Age aptitude questions involve using Algebraic Equations to determine the age of an individual based on the given data. While they may seem confusing at first, practice and a good understanding of the underlying concepts can help candidates become proficient in solving age-related problems.
By mastering problems of age, candidates can develop valuable problem-solving and analytical skills that can be applied in various aspects, making them well-prepared for a range of quantitative aptitude questions.
Here are some formulas and tricks to solve age problems that can make it simple for candidates to solve problems with ease:
- An individual’s age after n years will be (x+n) years old, and their age before n years will be (x-n) years if their present age is x.
- The age of one person can be considered as px and the age of the other person as qx, if the age is expressed as a ratio of p:q.
- If a person is currently x years old, they will be (x + n) years old in n years.
- If a person is currently x years old, then 1/n of their age will be (x/n) years.
By mastering these tricks and formulas, you can easily solve various age-related problems and improve your quantitative aptitude skills.
Shortcut Tricks for Problems on Ages
For easy calculation, we can use the method below:
The above image demonstrates a shortcut method. Here’s how it works in simple steps
Image 1:
Step 1: We have two people, A and B. Their age ratio now is 3:2. After 10 years, their age ratio will be 4:3.
Step 2: Look at the ratios (3:2 and 4:3). Notice the difference between the numbers. For A, it’s 3 to 4 (an increase of 1). For B, it’s 2 to 3 (an increase of 1). The difference is the same (1:1).
Step 3: Since the difference is 1:1, subtract the smaller ratio (3:2) from the bigger ratio (4:3). This gives (4 - 3):(3 - 2) = 1:1.
Step 4: The 1:1 difference matches the 10-year gap mentioned. So, each unit in the ratio stands for 10 years.
Calculate Ages:
For A: The present ratio is 3, so 3 × 10 = 30 years.
For B: The present ratio is 2, so 2 × 10 = 20 years.
Image 2:
Step 1: We have two people, C and D. Their age ratio 5 years ago was 4:1. At present, their age ratio is 3:1.
Step 2: Look at the ratios (4:1 and 3:1). Notice the difference between the numbers. For C, it’s 4 to 3 (a decrease of 1). For D, it’s 1 to 1 (no change). The difference needs adjustment due to the 5-year gap.
Step 3: To account for the difference, rationalize the ratios by multiplying. For the past ratio (4:1), multiply by 2 to get 8:2. For the present ratio (3:1), multiply by 3 to get 9:3. Then subtract (9 - 8):(3 - 2) = 1:1.
Step 4: The 1:1 difference matches the 5-year gap mentioned. So, each unit in the ratio stands for 5 years.
Calculate Ages:
- For C: The rationalized present value is 9, so 9 × 5 = 45 years.
- For D: The rationalized present value is 3, so 3 × 5 = 15 years.
Examples - Ages
Example 1:
Problem Statement: B’s age after 10 years would be equal to 4 times his age 2 years ago. What will be his age 5 years from now?
Solution:
Let B’s present age be m years.
According to the question:
m + 10 = 4(m − 2)
m + 10 = 4m − 8
3m = 18
m = 6
Thus, B’s present age is 6 years.
Therefore, B’s age 5 years hence = 6 + 5 = 11years.
Example 2:
Problem Statement: The ratio of the present ages of C and D is 5: 6. After 10 years, this ratio will become 6: 7. Find the present ages of C and D.
Solution:
Let the common ratio be m.
Thus, C's present age = 5m years,
and D's present age = 6m years.
According to the question:
5m + 10/6m + 10 =6/7
Cross-multiplying gives:
7(5m + 10) = 6(6m + 10)
35m + 70 = 36m + 60
35m - 36m = 60 - 70
-m = -10
m = 10
Thus, C's present age = 5m = 50years,
and D's present age = 6m = 60years.
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