## Problems Based on Present Age Shortcut Tricks

### Example 1 :

Ratio of ages of M & N 4 years ago was 3 : 5. If the sum of present ages of M & N is 64 years than , Find the present ages of M & N.
Let the ages is M & N 4 years ago are 3x and 5x.
Hence,
( 3x + 4 )+( 5x + 4 ) = 64 years,
= 8x + 8 = 64, = 8x = 56, x = 7.  ( we get the value of x).
So the age of M , 4 years ago  = 7 x 3 = 21years,
and the age of N, 4 years ago = 7 x 5 = 35 years.
Now the present age of M is = ( 21 + 4 ) = 25 years,
and present age of N is = ( 35 + 4) = 39 years.

### Example 2 :

Ratio of ages of M & N 4 years ago was 3 : 5. If the sum of present ages of M & N is 64 years than , Find the present ages of M & N.
Step1:  M : N = 3 : 5 , According to Question ( P + Q ) = 64 years.
Sum of both ages 4 years ago is ( 64 – 8 ) = 56 , (say that before age that’s why subtract)
Step2:  M = ( 56 / 8 ) x 3 = 7 x 3 = 21 years
and N = (56 / 8 ) x 5 = 5 x 7 = 35 years,
Step3:  present age of M = ( 21 + 4 ) = 25 years
and present age of N = ( 35 + 4 ) = 39 years.

### Example 3 :

At present , the ratio between the ages of Anil and  Anu is 4 : 3 . After 4 years , Anil’s age will be 24 years . What is the age of Anu at present ?
Let the present age of Anil and Anu is 4x years and 3x years respectively.
So , After 4 years Anil’s age ,will be 24 ,
4x + 4 = 24
4x = 20
x = 5
So , Anu present age is 3x = 3 x 5 = 15 years .

### Example 4 :

The total age of gangotri ,sabir, and bibhas is 96 years.10 years ago , the ratio of their ages was 2 : 4 : 5.What is the present age of bibhas?
Step 1: Let 10 years before gangotri, sabir, and bibhas ages 3x, 4x, 5x years respectively.
Then ( 2x + 10 ) + ( 4x + 10 ) + ( 5x + 10 ) = 96,
= 11x = 66 = x = 6.
Step 2:  Bibhas present age is ( 5x + 10 ) = ( 5 x 6 + 10 ) = 40 years.

### Example 5:

Present age of  Ramesh and Suresh are in ratio 5 : 6 respectively . Six years  hence , the  ratio of their ages will become 6 : 7 respectively . What is Ramesh present age in years ?
Let the present age of  Ramesh and Suresh 5x and 6x years respectively.
So , 5x + 6 / 6x + 6 = 6 / 7
7(5x + 6) = 6 (6x + 6)
36x + 36 = 35x + 42
x = 6
Ramesh’s present age is 5x = 5 x 6 = 30 years .

### Example 6:

Seven years ago , the age ratio of Sonu and Monu was 6 : 5 . Three years hence , the ratio of their ages will be 11 : 10 . What is Monu ‘s age at present ?
Let the age of Sonu and Monu 7 years ago be 6x and 5x years respectively .
So, (6x  + 7) + 3 /(5x + 7 ) + 3   = 11 / 10
10 ( 6x + 10) = 11 ( 5x + 10 )
5x = 10
x = 2
So, Monu’s present age  = ( 5x + 7 ) = 17 years .

### Example 7 :

twelfth years hence , Rahul will be just five times as old as he was 12 years ago , His present age is ?