Age-Based Problems: Shortcuts & Tricks | Quantitative Techniques for CLAT PDF Download

Problems on ages – basics and concept         

Problems on ages basically consist of information about the ages of two or more persons and a relationship between their ages in the past/present/future.

In the quantitative aptitude section the problems on ages are kind of brain teasers,  at the very first time when a candidate studies this it may seem to be complex, but it becomes easy when solved step by step.
In the quantitative aptitude sector problems on ages mostly are asked for 2-3 marks but there may be a possibility of age-based questions being asked as a part of the data sufficiency or data interpretation. So it is very important to clarify the concept to each and every candidate. 

Useful tips and tricks to solve the problems of ages

The useful tips given below are for the Candidates who are not much familiar with the concept and tendency to skip the problems on ages or answer them incorrectly. These tips may help you to clear the concept and answers the questions correctly.

1. To read the question carefully and gradually form the equation is the most important thing. It helps you answer the question.
2. Basic things like subtraction, addition, multiplication, and division will help a candidate reach the answer and no complicated calculations are required to answer these questions.
3. Arrange the values correctly and use them as linear equations.
4. Once the linear equation has been formed, solve the equation to find the answer.
5. The final step is to recheck the answer obtained by placing it in the equation formed to ensure that no error has been made while calculating.

The ‘problems on ages’ is one such topic which is not just asked in the preliminary phase of the examination but questions from this topic may also be asked in the main examination in a rather complex manner.

Important Formulas

The formulas given below are related to the problems on ages which may help you to answer the problems quicker and also get a better idea of the concept:-

1. Suppose if the present age of a person is x, then after n years, the age of the person will be (x+n) years.
2. Suppose if the present age of a person is x, then before n years the age of the person will be (x-n) years.
3. Suppose the ratio of two persons is p : q, then their age will be px and qx respectively.
4. Suppose the present age of a person is x, then  n times the present age will be (x * n) years
5. Suppose the present age of a person is x, then 1/n of the age shall be equal to (x/n) years

These formulas and tricks will help you in solving the questions easily and more efficiently.

Examples

Q1: The present ages of the three friends are in the ratio 3 : 5 : 7. Eight years ago, the sum of their ages was 96. find the sum of the present ages of the first two friends (in years)?
(a) 42 years
(b) 64 years
(c) 70 years
(d) 67 years
(e) None of these
Ans: e
Sol: Let the present age of three friend’s are = 3x, 5x and 7x
(3x – 8) + (5x – 8) + (7x – 8) = 96
15x – 24 = 96
15x = 120
x = 8
Their present ages are 24 years, 40 years and 56 years respectively.
The sum of the present ages of the first two friends = ( 24 + 40) = 64 years
Hence, option B is correct.

Q2: The total ages of Aman, Nageshwar and Satyam is 96 years. The ratio of their ages before 5 years was 2 : 3 : 4. What is the present age of Aman?
(a) 23 years
(b) 32 years
(c) 21 years
(d) 33 years
(e) None of these
Ans: a
Sol: Let the ages of Aman, Nageshwar and Satyam 5 years ago be 2x, 3x and 4x years respectively.
So, total of their present ages will be,
(2x + 5) + (3x +5) + (4x + 5) = 96
=> 9x + 15 = 96
=> 9x = 81
x = 9.
So, the present age of Aman =( 2x + 5 )=( 2 × 9 + 5 )= 23 years.
Hence, option A is correct.

Q3: Five years ago the ratio of the ages of Amit and Neha was 8 : 7. Three years hence, the ratio of their ages will be 12 : 11. what is Neha’s age at present?
(a) 13 years
(b) 16 years
(c) 8 years
(d) 19 years
(e) None of these
Ans: d
Sol: Let the age of Amit and Neha five years ago 8x and 7x respectively.
Amit’s present age = (8x + 5)
Neha’s present age = (7x + 5)
Now, as per the equation,
{(8x + 5) + 3} /{( 7x + 5) + 3} = 12/11                        
=> (8x + 8)/(7x + 8) = 12/11
=>  88x + 88 = 84x + 96  
=>  4x = 8  
⇒  x = 2.  
 ∴     Neha’s present age = (7x + 5) = (7 × 2 + 5) = 19 years.
Hence, option D is correct.

Tricks:-
Amit : Neha =  8 : 7      ( -5)
= 12 : 11   (+3)
= ( – 5 + 3 ) = 2
So, Neha’s age = 7 × 2 = 14
Neha’s present age = 14 + 5 = 19 years  
Or, Neha’s age = 11 × 2 = 22
Neha’s present age = 22 – 3 = 19 years

Q4: The ratio of the father’s age to his son-in-law’s age is 9 : 5. The product of their ages is 1125. The ratio of their ages after five years will be :
(a) 1 : 3
(b) 2 : 3
(c) 3 : 4
(d) 5 : 3
(e) None of these
Ans: d
Sol:
Let the present ages of Father and son-in-law be 9x and 5x respectively.
9x × 5x = 1125      
45ײ = 1125      
x² = 25  
x = 5.
Required ratio  = (9x + 5) : (5x + 5)  ⇒   50 : 30  ⇒  5 : 3.  
Hence, option D is correct.

Q5: The ratio of the present ages of two boys is 2 : 3 and six years back, the ratio was 1 : 3. What will be the ratio of their ages after 4 years ?.
(a) 1 : 3
(b) 3 : 4
(c) 2 : 3
(d) 3 : 5
(e) None of these
Ans: b
Sol: Assume 2x and 3x be the present age of two friends respectively.
Then,
2x – 6  = 1 3x – 63
⇒ 6x – 18 = 3x – 6  
⇒  3x  = 12  
⇒  x = 4.
So,  required ratio = (2x + 4) : (3x + 4)  ⇒  12 : 16  ⇒  3 : 4.  
Hence, option B is correct.
Tricks :-

So, the present ages of the two boys 8 years and 12 years respectively.
4 years later their ages will be (8+4) = 12 years and (12+4)= 16 years.
Ratio = 12 : 16 = 3 : 4.