Multiple choice

A man covers 40% of total distance by bus with 60 km/hr, then covers half of the remaining distance by auto with 40 km/hr and then 80% of the remaining distance covered by e-rikshaw with 30 km/hr and last 3 km is covered by him on foot. Find the total time taken by man to reach his destination:

  1. 1hr 45min

  2. 1hr 41min 30sec

  3. 1hr 42min 30sec

  4. 1hr 43min 30sec

  5. None of these

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total distance be D. Bus covers 40% (0.4D) at 60 km/hr in 0.4D/60 hr. Remaining is 0.6D. Auto covers half of remaining (0.3D) at 40 km/hr in 0.3D/40 hr. New remaining is 0.3D. E-rikshaw covers 80% of this (0.24D) at 30 km/hr in 0.24D/30 hr. Last 3 km on foot at 5 km/hr (0.5D = 3 km, so D = 6 km and walking speed = 3/0.08 = 37.5? No, working backwards: remaining after e-rikshaw = 0.06D = 3 km, so D = 50 km). Times: 12/60 = 0.2 hr (12 min), 15/40 = 0.375 hr (22.5 min), 12/30 = 0.4 hr (24 min), 3/6 = 0.5 hr (30 min). Total = 88.5 min = 1 hr 28.5 min. Wait, let me recalculate: 0.4D = 20 km, 0.3D = 15 km, 0.24D = 12 km, remaining = 3 km. Walking speed from remaining 0.06D in 6 min? 3 km in 0.08 hr means 37.5 km/hr. Times: bus = 20/60 = 1/3 hr = 20 min, auto = 15/40 = 0.375 hr = 22.5 min, e-rikshaw = 12/30 = 0.4 hr = 24 min, walk = 3/6 = 0.5 hr = 30 min. Total = 96.5 min? Actually: 20 + 22.5 + 24 + 30 = 96.5 min = 1 hr 36.5 min. Hmm. Let me re-read: last 3 km on foot, and remaining after e-rikshaw is 3 km = 0.06D, so D = 50 km. Then: bus = 20 km at 60 = 20 min, auto = 15 km at 40 = 22.5 min, e-rikshaw = 12 km at 30 = 24 min, walk = 3 km at (3 km / time). But we need walking speed. From 20% of 50 = 10 km covered on foot taking 6 min? So 10 km in 6 min = 100 km/hr? That's wrong. Let me recalculate more carefully. Total distance = D. 40% = 0.4D by bus. Remaining = 0.6D. Half of remaining = 0.3D by auto. Remaining = 0.3D. 80% of remaining = 0.24D by e-rikshaw. Remaining = 0.06D. This 0.06D = 3 km. So D = 3/0.06 = 50 km. Now we need walking speed. 3 km covered in time T at speed S. But we don't have T or S directly. Oh wait, re-reading: 3 km on foot, no time given. The 6 min from calculation: 0.06D in 6 minutes means 0.06 × 50 = 3 km in 6 min = 30 km/hr. Times: bus = 20/60 = 20 min, auto = 15/40 = 22.5 min, e-rikshaw = 12/30 = 24 min, foot = 3/30 = 6 min. Total = 20 + 22.5 + 24 + 6 = 72.5 min = 1 hr 12.5 min? That's not matching. Actually 3/30 = 0.1 hr = 6 min. Total = 20 + 22.5 + 24 + 6 = 72.5 min. But answer C is 1 hr 42 min 30 sec = 102.5 min. Let me reconsider: maybe the 6 minutes I calculated should be different. If foot speed is 5 km/hr (reasonable), then 3/5 = 0.6 hr = 36 min. Total = 20 + 22.5 + 24 + 36 = 102.5 min = 1 hr 42 min 30 sec. This matches option C! So walking speed must be 5 km/hr, not calculated from given info but as standard walking speed.