Problems on Ages with Shortcuts

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Age, a period of human life measured by years from birth, some people have 15 years, some may have 32 years and some good people like me always have 22 years (of course I am 22 from last 3 years, now don't ask me how). Generally you may get 3 replies when you tried to know anybody's age.

1. They may tell you their true age.
2. They may tell you some false and standard age (like me).
3. Or you may return rubbing your cheek with sad face if the answerer was an unknown girl.

But, the people in our competitive exams are lil different. They wont answer any question in direct manner. Instead of it saying a number, they just will say you some fraction or ratio, or just link their age to their relatives' or friend's age and ask you to guess their age. Ofcourse it sounds irritating. Usually we give a dirty look at the person and let him / her go in their way. But in exams, we don't have any other option except finding their real age. So here are some shortcut techniques to made the process of finding ages easier.We shall discuss the tricks with some examples so that you easily can understand them.

1. The average age of Khan, Kapoor, Kumar, Bachhan and Roshan is 28 years. The average age of Bachhan and Roshan is 25 years. What is the average age of Khan, Kapoor and Kumar ?

Solution :

Here 5 persons' average ( Khan, Kapoor, Kumar, Bachhan and Roshan) age is  = 28 Years.

That means their total age = 5 X 28 = 140 Years.

similarly, average age of two persons (Bachhan and Roshan)  is 25 years.

So their total age = 25 X 2 = 50 Years.

here 140 years is the total age of 5 persons             ( Khan, Kapoor, Kumar, Bachhan and Roshan)
50 years is the total age of 2 persons (Bachhan and Roshan)

So obviously, the total age of Khan, Kapoor and Kumar = Total age of  ( Khan, Kapoor, Kumar, Bachhan and Roshan) - Total age of (Bachhan and Roshan)

= 140-50 = 90 years.

But here we need average age of these 3 persons.

=> 90/3  = 30 Years

Shortcut Method :

((5 X 28) - (2 X 25)) / 3 =  (140-50)/ 3 = 90/3 = 30 Years


2. The ratio between the ages of Kareena and Sonam is 5:8 respectively and difference between their ages after 5 years will be 12 years. What is the present age of Kareena ?

Solution :
Usually for these type of questions people start with present age as X and adding 5 to get the ages after 5 years and later solve those equations. But its very time consuming.

A simple logic here is if the age difference between you and your friend is 8 years, after 5 or 10 years also the difference will be same. Hope you are getting what I am trying to say ;)

now see, the ratio between their ages is 5 : 8 

That means their actual ages will be some 5X and 8X

Then the difference between their ages is 5X-8X
in the question it is given that the difference is 12 years =>  5X-8X = 12  => 3X=12  => X = 4

So obviously Kareena's age = 5(4) = 20


3. Abhi is 30 years younger than his mother Jaya. Five years ago, Abhi was 1/4 as old as his mother was. How old is Abhi today ?

Solution :

5 years ago the ratio between their ages was Abhi : Jay a= 1X : 4X

we know that Hari is 30 years younger than Jaya. That means the difference between their ages is 30.

=>   3X = 30  => X = 10.

But this is the age of 5 years ago. So, the present age will be =10+5 = 15 Years

4. At present the ratio of the ages of Anand and Milind is 4 : 7 respectively. 6 years hence it will be 7 : 10 respectively. What is the present age of Milind ?

Solution :

Present ratio of their ages is 4 : 7 (So their present ages will be 4X, 7X)

After six years it will be of 7 : 10

=> (4x+6) : (7x+6) = 7 : 10

=> 40x + 60 = 49X + 42 (Cross Multiplication)

=> 9x = 18

=> x = 2                          

So Milind's present age will be 7X2 = 14 Years

Shortcut :

There is a shortcut formula for finding X

here, New ratio difference is 3, Added number is 6 (years)
Cross multiplication difference is 49-40 = 9

=>       X = (3 x 6) / 9  = 2



So Milind's present age will be 7X2 = 14 Years

5. Ten years ago the ratio between the ages of Mohan and Suman was 3:5 respectively. 11 years hence it will be 11:16 respectively. What is the present age of Mohan?

Solution :

 10 years ago 3x : 5x  -------------> Old Ratio

11 years hence  11x : 16x       ------------->  New Ratio

here the difference between ages is 21 years (10 years ago + 11 years hence)

apply above formula here

New ratio difference is (16-11) = 5

Added or substracted number (difference between ages) is = 21

Old and new ratios cross multiplication difference is = 55 - 48 = 7

==> X = (5 x 21) / 7 = 15

present age of mohan is = his age of 10 years ago + 10
                               
                                            = 3x15 + 10 = 55 years

6. Amar is as much younger than Raja as he is older than Kiran. If the ages of Amar and Raja are 30 years and 36 years respectively, what is the age of Kiran now ?

Solution :
Simple logic....
Amar is as much younger than Raja as he is older than Kiran. Try to understand this sentence. According to this sentence you can understand that

• Amar is younger than Raja that means there is some X years difference between Amar and Raja.
• Amar is older than Kiranwith same age difference (X years) between Amar and Kiran.

But we know that the ages of Amar and Raja are 30 and 36 years.

So the difference between their ages is = 6 years

So the difference between Amar and Kiran should be = 6 years.

We know the age of Amar as 30 years and Kiran is younger than Amar for 6 years. So he should be of 24 years.

With a single glance you can calculate answer for these type of problems.


7. The average age of a class of 20 students is 20 years. When the age of the teacher is also included, the average will be increased by 2 years. What is the age of the teacher ?

Solution :
Simple logic,
we know that 20 students' average = 20 years
20 people total age = 20 x 20 = 400 years

Including Teacher's

21 people average = 22 years

21 people total age = 21 x 22 = 462

we know the age of 20 students = 400 Yeras

we know the age of 21 people (20 students+ Teacher) = 462

so the age of Teacher will be 462-400 = 62 Years

8. The average age of a wife and husband, who were married 10 years ago, was 20 years then. Including a child the present average age of the family is 23 years. What is the present age of the child?

Solution :

10 year's ago average age = 20 years
10 year's ago total age = 20 x 2 = 40 years.

to calculate their present total age, you should add 20 (10 for wife and 10 for husband) to the age of 10 years ago

=> 40+20 = 60 years (this is the present age of husband and wife)    ----------- (1)

according to the given data, present average age of the family of 3 members is = 23 years

so Total age of 3 members = 23 x 3 = 69 years. ------------------(2)

but we know the present age of Husband and Wife = 60 years

so from equations (1) and (2), we can get the present age of the child is = 9 years


9. Five years ago the average age of a family of five members was 27 years then. Including a child the present average age is still same today. What is the age of the child now ?

Solution :

5 years back average = 27 years

present average should be 5 +27 = 32 Years

So total age of the 5 members at present = 5 x 32 = 160 years  -----------------(1)

but its given that including the child, the present average is 27 years.

=>   the total age of 6 members at present = 6 x 27 = 162 years -----------------(2) 

so from (1) and (2), you can easily get that the present age of the child is 2 years



10. The ratio between the ages of Karan and Arjun is 9:5 and sum of their ages at present is 56 years. How old will karan be after 4 years ?

Solution :

according to given data their ages should be 9x, 5x

their present age = 9x+5x = 56  ==> 14x = 56

so x = 4

so present age of Karan is 9 x 4 = 36 years

after 4 years, 36+4 = 40 years :)


Note : To explain the calculation process in clear, we have mentioned these many steps for every problem. But in exams you should do almost all of these calculations mentally and try to avoid writing every single step.

That's all for now friends. Hope we made the concepts of Ages easy now. Feel free to use the comments box below to reach us if you  have any doubts. We will answer. All the best and happy reading :)

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