10 years ago , the ratio of age of A to that of B was 4 : 5. Ten years hence, the ratio of age of A to that of B will be 6 : 7. If at present C is 10 years younger than B , then what will be ratio of present age of A to that of C ?

1 : 1  

( 10 years ago )                  A    :    B 

                                          4    :    5

present age of A = 4x + 10 , present age of B = 5x + 10 

according to question , after 10 years 

                                         A    :   B

                                         6    :    7

i.e. \(\frac{4x\;+\;20}{5x\;+\;20}\)  =   \(\frac{6}{7}\)

 28x + 140 = 30x + 120 

 2x = 20 

 x = 10 

as , A's present age = 4x + 10 

 A's present age =>  40 + 10 = 50

B's present age =>  5×10 + 10 = 60

It is given that C is 10 years younger than B 

 So, C's present age =>   60 - 10 = 50    

Ratio of    A   :   C

               50 :   50

               1   :     1