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Examples with Short Tricks 1

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

= 3×15 + 10 = 55 years