Given:
Speed of walking = 10 km/hr
Speed of auto = 30 km/hr
Formula Used:
Distance = Speed × time
Calculation:
Total distance covered = 10 × 18 = 180 km
Let the time to cover distance by walk be x hour
So, The time to cover distance by auto = (10 - x) hr
According to the question
10x + 30(10 - x) = 180
⇒ 10x - 30x + 300 = 180
⇒ -20x = -120
⇒ x = 6 hrs
So time taken to cover distance by auto = 10 - 6 = 4 hrs
Distance traveled by auto = 30 × 4 = 120 km
∴ the correct answer is option 3.
Alternate Method
Formula used:
Speed=TimeDistance
Calculation:
Total distance covered = 10 × 18 = 180 km, Sw = 10 km/hr, Sa = 30 km/hr
Let the distance overed by walk, Dw = 180 - Da, distance overed by auto, Da
Time required by auto = Ta, Time required by walk = Tw
Speed by auto,
Sa=TaDa
30=TaDa.............(1)
Speed by walk,
Sw=TwDw
But, total time, Tt = Ta + Tw = 10 hrs, So, Tw = 10 - Ta,
Total distance, Dt = Da + Dw = 180 km, Dw = 180 - Da
10=10−Ta180−Da
10(10 - Ta) = 180 - Da
From equation (1), Ta=30Da
Threrfore, 10(10−30Da)=180−Da
(100−3010Da)=180−Da
Da = 120 KM