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Present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6. Find their present ages.

let the age of Anu be 4x years and age of Raj be 5x years.

after 8 years age of Anu will be (4x+8)years and age of Raj will be (5x+8)years

according to question:

therefore the present age of Anu=4*8=32 years

the present age of Raj = 5*8=40 years

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 Hello Charan, 

As the ratio is given 4:5, the ratio must have been obtained by dividing both the numerator and denominator of the fractional number with the same number. So let that number be x.

It is given in the question above that after 8 years there ages will be in the ratio 5:6.

So the equation will be like this :
 
4x + 8         5
--------     = --               [ The hyphens are used as a line as there is no provision for writing fractional numbers 
5x + 8         6                  here ]
 
After cross multiplying : 
6 ( 4x + 8 )   =   5 ( 5x + 8 )
24x + 48 = 25x + 40
48 - 40 = 25x - 24x
8 = x 
Therefore, x=8
 
So, the present ages of Anu and Raj :
Anu's age = 4x = 4 * 8 = 32 
Raj's age = 5x = 5 * 8 = 40
 
Hope it helps !!!!!!! All the best !!!!!!!!
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