Question 550396
Let speed of the current of the river be "x" kph

Hence time taken by motor boat up the river = 100/(60-x)

Similarly time taken by motor boat down the river = 100/(60+x)

Since total time taken by motor boat is 12 hrs, therefore
100/(60-x)+ 100/(60+x) = 12

Cross multiplying above eqn by the terms in denominator results in.....
{100*(60+x)}+ {100*(60-x)} = 12*(60+x)*(60-x)
>6000 +100x+6000-100x= 12(3600-x^2)
>12000 = 12(3600-x^2)
Dividing above eqn by 12...
> 1000 = 3600-x^2
Transposition results in
>x^2= 3600-1000
> x^2 = 2600
Therefore x = +-50.99 say 51

As the speed can not be -ve, therefore speed of the current of the river= 51kph