Gagan traveled a certain distance at his regular speed. If he had increased his speed by 20 km/h, he would have taken 2 hours less to complete the journey. On the other hand, if his speed had been reduced by 10 km/h, it would have taken him 1 hour and 36 minutes longer to cover the same distance. Determine the time Gagan usually takes to travel this distance.

Let car covers 'D' km with 'v' km/h in 'T' hours. Using, distance = speed X time We have, 'D' = vT ----- (I) ATQ: We have, (v + 20) X (T - 2) = 'D' ---------- (II) And, (v - 10) X (T + 1.6) = 'D' ----- (III) (1 hour 36 minutes = (96/60) = 1.6 hours) Using equation (II) and (III) , We have, (v + 20) X (T - 2) = (v - 10) X (T + 1.6) Or, vT - 2v + 20T - 40 = vT + 1.6v - 10T - 16 Or, 3.6v - 30T + 24 = 0 Or, 6v - 50T + 40 = 0 --------- (IV) Using equation (I) and (II) , We have, (v + 20) X (T - 2) = vT Or, vT - 2v + 20T - 40 = vT Or, v - 10T + 20 = 0 ------ (V) On solving equation (IV) - 6 X equation (V) , We have, (6v - 50T + 40) - 6 X (v - 10T + 20) = 0 Or, 6v - 50T + 40 - 6v + 60T - 120 = 0 Or, 10T = 80 Or, 'T' = 8 hours