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?
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? Correct Answer 110 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 = 110
car speed is 110 km/h.
Important Points
When a quantity increased by m%,
New value = (1 + (m/100)) × old value
