Let the speed ofSagar be considered as x km/hr.And speed of Aakash be y km/hr.Therefore, time taken by Sagar = 2/x hrs.And time taken by Aakash = 2/y hrs.Now, according to the question.2/x - 2/y = 2/601/x - 1/y = 1/60 ..................(1)(y - x)/xy = 1/6060(y - x) = xy ...................(2)

Now, according to the second condition.Speed of Sagar = (x + 2) km/hr.Speed of Aakash = (y - 2) km/hr⇒ (2/y-2) - (2/x+2) = 2/60⇒ (1/y-2) - (1/x+2) = 1/60⇒ {(x+2-y+2)/(y-2)(x+2)} = 1/60⇒ 60(x-y+4) = xy+2y-2x-4Now, substituting the value of xy in the above, we get.⇒ 60(x-y+4) = 60(y-x)+2y-2x-4⇒ 30(x-y+4) = 30(y-x)+y-x-2⇒ 30x-30y+120 = 30y-30x+y-x-2⇒ 30x+31x-30y-31y = -2-120⇒ 61x-61y = -122⇒ x-y = -2⇒ x = y-2Substituting the value of x in (1), we get.⇒ {1/(y-2) - (1/y) } = 1/60⇒ (y-y-2)/(y²-2y) = 1/60⇒ y²-2y = 120⇒ y²-2y-120 = 0⇒ y²+10y-12y-120 = 0⇒ y(y+10) -12(y+10) = 0⇒ (y+10) (y-12) = 0⇒ y = -10 is not possible. So, y = 12 is correct value.Substituting the value of y = 12 in x = y - 2, we get.⇒ x = 12 - 10⇒ x = 10So, speed of Sagar in the first round was 10 km/hr and speed of Aakash was 12 km/hr.