Question

Karan always reaches his office 30 minutes after the office starting time. When he increased his car speed by 20%, he arrived at the office starting time. But when he increased his car speed by 10 km/h he failed to reach the office on time and only arrived at the office 15 minute after the starting time. What could be the usual car speed?
1. 9 km/h
2. 10 km/h
3. 11 km/h
4. 12 km/h

Answer 1

Correct Answer - Option 3 : 11 km/h

Calculation:

Let t be the usual time taken and u is the usual speed and d is the distance,

⇒ d/u = t

When speed increased by 20%

⇒ u₁ = 1.2u

⇒ time = t - 0.5

d = 1.2u × (t - 0.5)

⇒ 1.2ut - 0.6u

∴ ut = 1.2ut - 0.6u

⇒ 0.2ut = 0.6u

⇒ t = 3hrs

when u₂ = u + 10

⇒ time = t - 0.25 = 2.75

∴ d =  (u + 10) × (2.75) = 2.75u + 27.5

⇒ 3u = 2.75u + 27.5 

⇒ u = 11 km/h  

∴ The usual car speed is 11 km/h.

When a quantity increased by m%,

New value = (1 + (m/100)) × old value