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The usual average speed of a car on a particular stretch of road is 75 km/hr. On a particular day, the average speed was 12% less than the usual, as a result of which the time taken was 18 minutes more. How long is the stretch of road, in kilometres?

The usual average speed of a car on a particular stretch of road is 75 km/hr. On a particular day, the average speed was 12% less than the usual, as a result of which the time taken was 18 minutes more. How long is the stretch of road, in kilometres? Correct Answer 165

Detailed Solution:

18 min = 3/10 hr

Speed = 75 km/hr

Speed after decreasing = 75 × (88/100) = 66 km/hr

Let the distance be D, then

According to the question:

⇒ D/66 – D/75 = 3/10

⇒ D = 3/10

⇒ D = (10/3) × (75 × 66)/9 = 165 km

Short trick:

Speed ratio before and after decrement of speed = 75 : 66 = 25 : 22

As we know, Time is inversely proportional to speed, then

Time ratio before and after decrement of speed = 22 : 25

According to the question

⇒ 25 – 22 unit = 18 min

⇒ 3 unit = 18 min

⇒ 22 unit = 6 × 22 = 132 min

So, total time = 132/60 hr

As we know,

Distance = Time × speed

Distance = 132/60 × 75 = 165 km

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