Question

The age of two persons A and B are in the ratio of 8:5. After 12 years the ratio will become 10:7.  What  is the present age of A?

Answer 1

let their original present  ages of A and B  be 8x yrs and 5x yrs respctively
 after 12 years,
age of A=[8x +12] yr
age of B=[5x + 12] yr
but the ages given in the problem = 10 x yrs and 7x yrs
$=>$10/7 =8x + 12 / 5x +12
       =10 [ 5x + 12] = 7[8x +12 ]
       = 50x + 120 = 56x + 84
       = 56x - 50x = 120 - 84
       = 6x = 36
       = x=36/6
       = x = 6
therefore, present age of A = 8x = 8 * 6 = 48

so A is 48 years old presently.

Answer 2

let the present ages of A and B be 8x , 5x repectively
after 12 years
                 8x+12/5x+12 = 10/7
                       ( 8x+12 )  7 = ( 5x+12 ) 10
                            56x+84 = 50x+120
                                       6x = 36
                                          x = 6
                   Present Age of x = 8x
                                               = 8*6
                                                = 48 years