Question

The total distance between metropolis A and metropolis B is 800 km. A person covers 50% of the complete distance at 10 km/hr, 1/4th of the remaining distance at 20 km/hr and the remaining distance at s km/hr. If the average speed of the person during total journey is 14(6/11) km/hr, then, the value of s, is –

1. 20
2. 30
3. 40
4. 25

Answer 1

Correct Answer - Option 2 : 30

Calculation:

Total distance between A and B = 800 km

(i) Speed for first 50% distance (400 km) = 10 km/hr

(ii) Speed for next 1/4^th of the remaining distance (400/4 = 100 km) = 20 km/hr

(iii)Speed for the remaining distance (300 km) = s km/hr

Average Speed = (Total Distance)/ (Total Time)

Total Time = (400/10) + (100/20) + (300/s)

⇒ (40 + 5 + 300/s)

⇒ (45 + 300/s)

∴ Average Speed = 800/ (45 + 300/s)

⇒ 14(6/11) = 800/ (45 + 300/s)

⇒ 160/11 = 800/ (45 + 300/s)

⇒ 160/11 = 800s/ (45s + 300)

⇒ 1/11 = 5s/ (45s + 300)

⇒ 45s + 300 = 55s

⇒ (55s – 45s) = 300

⇒ 10s = 300

⇒ s = 300/10

⇒ s = 30 km/hr

∴ The value of s is 30 km/hr.