Ages

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.

Age Problem Formulas

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.

Ages - Questions and Answers

Question 1: 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.

Question 2: 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.

Question 3: A's age after 15 years would be equal to 5 times his age 5 years ago. Find his age 3 years hence.

Solution :

Let A's present age be 'n' years.
According to the question,
n + 15 = 5 (n - 5)
=> n + 15 = 5 n - 25
=> 4n = 40
=> n = 10
=> A's present age = 10 years
Therefore, A's age 3 years hence = 10 + 3 = 13 years

Question 4: The product of the ages of A and B is 240. If twice the age of B is more than A's age by 4 years, what was B's age 2 years ago?

Solution : 

Let A's present age be x years. Then, B's present age = 240 / x years
So, according to question
2 (240 / x ) - x = 4
=> 480 - x² = 4 x
=> x² + 4 x – 480 = 0
=> (x + 24) (x - 20) = 0
=> x = 20
=> B's present age = 240 / 20 = 12 years
Thus, B's age 2 years ago = 12 - 2 = 10 years

Question 5 : The present age of a mother is 3 years more than three times the age of her daughter. Three years hence, mother's age will be 10 years more than twice the age of the daughter. Find the present age of the mother.

Solution : 

Let the daughter's present age be 'n' years.
=> Mother's present age = (3n + 3) years
So, according to the question
(3n + 3 + 3) = 2 (n + 3) + 10 
=> 3n + 6 = 2n + 16 
=> n = 10
Hence, mother's present age = (3n + 3) = ((3 x 10) + 3) years = 33 years

Also Check:

Ages Solved Questions - [Read Here!]

Test your Skills- [Quiz]