## Examples with Short Tricks 1

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 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

= 3×15 + 10 = 55 years