  # Age Problems

Age Problems are always tricky! One must read the question carefully to frame equations to solve Age Problems. In this article we will know ho to solve such age problems.

Age problems are one of the most important problems from the point of view of CAT exam. Age problems are algebra-based word problems, in which we need to find the relation between the past, present and future ages of people. One must know how to crack age problems in order to save time in CAT Exams. In this post, we will discuss age problems using the smart method which will help you save time in CATExam Trick behind Age Problems

Age is a concept which is based on the concept of ratio and proportion. We need to solve questions related to the age of persons.   Age Problem Solved using Smart Methods

Question: The present age of the father is 5 times the age of his son. Five years ago, the age of the Father was ten times the age of his son at that time. How old is the father at present?

1) 45 years      2) 40 years     3) 48 years     4) 49 years     5) None of these

Regular Method to solve Age Problem

Solution:

Step 1:

Let us assume father’s present age as F

Let us assume the present age of the son to be as S

Step 2:

As mentioned in the question, the present age of the father is 5 times the age of son

F = 5 x S    (i)

Step 3:

Now frame an equation now

( F – 5 ) = 10 ( S – 5)  (ii)

Step 4:

F – 5 = 10S  – 50

5S – 5 = 10S – 50

5S = 45

S =9

F = 9 x 5 = 45

Smart Method to solve Age Problems

Step 1:

To solve this question using the smart method, we need to understand the question carefully.

As mentioned in the question that the father’s age is 5 times the age of son, we can clearly make out that the father’s age should be a multiple of 5.

By this, we can easily eliminate the options which are not the multiples of 5.

Therefore, option 3 and option 4 are eliminated.

Step 2:

Now we take the second condition into consideration and check which option satisfies the condition.

Option 1: 45 years.

If the father’s present age is 45 then the son’s age would be 9, since the father is 5 times the son’s age.

Now, five years ago father’s age would be 40 and son’s age would be 4.

Hence, the second statement states that 5 years ago father’s age was 10 times the age of the son.

As, 40 = 10 x 4; option 1 satisfies both the condition.

Therefore the father’s present age is 45.

Age Problem Solved using Smart Methods

Question: Father’s age is 25 years more than the son’s age. Four years hence, Fathers age will become 1 less than thrice the son’s age

What is father’s present age?

1)    31          2) 38         3) 34          4) 36  5) None of these

Regular Method to solve Age Problems

Solution:

Step 1:

Let us assume father’s present age to be as ‘F.’

Let us assume son’s present age to be as ‘S.’

As mentioned in the question father’s age is 25 years more than the son’s age.

F = S + 25            (i)

Step 2:

After 4 years,

Father’s age = F + 4

Son’s age = S + 4

Father’s age is 1 less than the thrice of son’s age

F + 4 = 3 (S + 4) – 1              (ii)

Step 3:

By substituting equation (i) in equation (ii) we get that,

F + 4 = 3 (F – 25 + 4) – 1

F + 4 = 3F – 63 – 1

2F = 68

F = 34 years.

Therefore, Father’s present age is 34 years.

Smart Method to solve Age Problem

To solve this question, we can check which option satisfies our condition and thus select the correct option.

Step 1:

Option 1: 31 years

If father’s age is 31 years then son’s age will be 31 – 25 = 6.

Now taking the second condition “Four years hence, Fathers age will become 1 less than thrice the son’s age”

After 4 years father’s age = 31 + 4 = 35 years

(3 + 4) x 3 = 20 years

Therefore, this option doesn’t satisfy our condition as 31 is not one less than 20.

Option 2: 38 years

If the father’s age is 38 years then the son’s age will be 38 – 25 = 13.

Now taking the second condition “Four years hence, Fathers age will become 1 less than thrice the son’s age”

After four years father’s age = 38 + 4 = 42

(13 + 4) x 3 = 51

Therefore, this option doesn’t satisfy our condition as 38 is not one less than 51.

Option 3: 34 years

If the father’s age is 34 years then the son’s age will be 34 – 25 = 9 years

Now taking the second condition “Four years hence, Fathers age will become 1 less than thrice the son’s age”

After four years father’s age = 34 + 4 = 38

(9 + 4) x 3 = 39

Therefore, this option satisfies our condition as 38 is one less than 39.

Hence, Option 3: 34 years is the correct answer.

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