Wednesday, 21 June 2017

Age Problems II – Problems on Age for SSC Exams

In this post, we will discuss Problems on Age that are frequently asked in SSC Exams and solve them in minimum time.
Problems on Age
Problems on age are the word problems that are solved framing equations. Making tables, framing equations are all conventional methods that take a lot of time in SSC Exams. Since SSC Exams have a time constraint; one should know the smart approach towards these problems.
In this post, we will discuss problems on age that are frequently asked in SSC Exams. These problems on age are solved using the smart method which will help you save time. Before moving further let's have a quick review of the basics of Age Problems. 
Problems on Age
Problems on Age: Example

Question: Ranjan’s and Anurag’s ages are in the ratio 4:5. Four years hence, their age ratio will become 5:6. What is Anurag’s present age?
1) 20 years     2) 16 years     3) 24 years      4) Data Insufficient       5) None of these

Solution:
Regular approach towards Problems on Age
Step 1:
Let us assume Ranjan’s  present age to be as R.
Let us assume Anurag’s present age to be as A.

Step 2:
As mentioned in the question, The ratio of Ranjan’s age to Anurag’s age is
R: A = 4: 5 => R/A = 4/5 => R = 4x ; A = 5x       (i)

Step 3:
As mentioned in the question, after 4 years
(R + 4)/ (A + 4) = 5/6             (ii)

Step 4:
By substituting equation (i) in equation (ii), we get
(4x + 4) / (5x + 4) = 5/6

Step 5:
By cross multiplication, we get
6(4x + 4)  = 5(5 + 4)
24x + 24 = 25x + 20
x = 4

Step 6:
By substituting the x value in equation (i) we get,
Anurag’s present age to be 5 x 4 = 20

Therefore, the correct answer is option 1; 20 years.

Smart Approach towards Problems on Age
Step 1:
Eliminate all the options that are not multiples of 5 because the options are on the basis of Anurag's age
Option 2 and 3 are not multiples of 5 so we eliminate both the options.
Option 4; Data insufficient is also eliminated as the data is sufficient to solve the problem.
Therefore the only options left are- options 1 and 5.

Step 2:
Option 1; 20 years – To verify whether this option is correct or not, we should know that the option should be a multiple of 5 and after 4 years his age should be a multiple of 6 [20 + 4 = 24]. Hence, this option satisfies both the conditions.

Therefore, the correct answer is option 1; 20 years.
Problems on Age
Problems on Age: Example

Question: The ages of Samina and Suhana are in the ratio of 7:3. After 6 years, the ratio of their ages will be 5:3. What is the difference in their ages?
1) 6 years       2)8 years        3)10 years        4) 12 years     5) None of these

Solution:
Regular approach towards Problems on Age
Step 1:  
Let us assume the present age of Samina be Sa
Let us assume the present age of Suhana be Su.

Step 2:
As mentioned in the question, the ratio of the ages of Samina and Suhana is       
Sa: Su = 7: 3 => R/A = 7/3 =>Sa = 7x Su = 3x       (i)

Step 3:
As mentioned in the question after 6 years, their ratio will be 5:3. 
This can be denoted as
(7x + 6)/( 3x + 6 ) = 5/3       (ii)

By cross multiplication we get,
21x + 18 = 15x + 30
6x = 12
x = 2

Step 4:
By substituting the value of x in the equation (ii) we get,
7x – 3x = (7 x 2) – (3 x 2) = 14 – 6 = 8

Therefore, the correct option is option 2; 8 years.

Smart Approach towards Problems on Age
Step 1:  
Let us assume the present age of Samina be Sa

Let us assume the present age of Suhana be Su

Step 2:  
As mentioned in the question, the ratio of the ages of Samina and Suhana is 
Sa: Su = 7: 3 => R/A = 7/3 => Sa = 7x Su = 3x 
Then the difference between their ages will be 
7x - 3x = 4x 

Step 3: 
By using the elimination method, eliminate options which don't satisfy the condition.
Option 1: years
If 6 years is the difference between Samina and Suhana then,
4x = 6 
x = 1.5 

Since in age problems the ages are considered to be an integer, we eliminate this option.

Option 2: 8 years
If 8 years is the difference between Samina and Suhana then,
4x = 8 
x = 2

Then Samina age will be 7 x 2 = 14 and Suhana age will be 3 x 2 = 6, 
As 14 - 6 = 8 years

Therefore, this option satisfies our condition.

Hence the answer is option 2: 8 years.

Problems on Age: Example

Question: After 5 years, the average age of a daughter and her mother will become 29.5 years. If today, the ratio of their ages is 2:5, what is the present age of daughter?

1) Cannot be determined      2) 25 years   3) 21 years    4)14 years    5) None of these

Solution:
Regular approach towards Problems on Age
Step 1:
Let us assume the present age of daughter to be as ‘D.’
Let us assume the present age of Mother to be as ‘M.’
Let us assume the present average to be as ‘A.’
The ratio of D: M = 2: 5

Step 2:
After 5 years,
The daughters age = D + 5
The mothers age = M + 5
The average of their age = A + 5 = 29.5 (As the numbers increase by 5, the average also increases by 5.

Step 3:
To find the present average we need to
(D + M) / 2 = 29.5 – 5
(D + M) / 2 = 24.5
D + M = 24.5 x 2
D + M = 49

Step 4: 
To find the present age of the daughter we need to multiply 2/7 (ratio of the daughter) with the present average.
D = 2/ 7 x 49
D = 14 years

Therefore, the correct answer is option 4: 14 years

Smart approach towards Problems on Age

This question can be easily solved using the smart method. 

In the question, the present ratio between the ages of the daughter and mother is 2: 5. 
The daughter's present age should be a multiple of 2.

Option 1: Can not be determined - The question contains all the necessary data to find the ages. Hence, this option is eliminated

Option 2: 25 years - Because 25 is not a multiple of 2, this option is eliminated.

Option 3: 21 years - Because 21 is not a multiple of 2, this option is eliminated.

Option 4: 14 years - 14 is a multiple of 2, therefore this option is taken into consideration.

By taking the second condition this option can be verified.

Therefore the correct answer is option 4: 14 years. 

Watch our expert faculty explain the smart method.




Practice Problems on Age for SSC Exams

Question: The ratio of ages of a couple is 4:3. After 4 years, this ratio will be 9:7. If at the time of marriage, the ratio was 5:3, then how many years ago were they married?

1) 10 years      2)12 years        3) 7years         4) 9 years          5) None of these

Question: The ratio between the present ages of Rajesh and Uma is 5:3 respectively. The ratio between Rajesh’s age 4 years ago and Uma’s age 4 years hence is 1:1. What is the ratio between Rajesh’s age 4 years hence and Uma’s age 4 years ago?

1) 2:1        2) 3:1       3) 5:2      4) 4:3      5) None of these

Do leave your answers in the comment section!

Stay tuned for our next post.
Problems on Age
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