A cyclist travels from City A to City B at an average speed of 20 km/h and takes 4 hours. If they want to complete the same journey in 2.5 hours, by what amount (in km/h) should they increase their average speed?

Correct — A. The route does not change, so find its length first, then the speed that covers it in 2.5 hours.

Distance = speed × time = 20 × 4 = 80 km
New speed = distance ÷ new time = 80 ÷ 2.5 = 32 km/h

Increase = new speed − old speed = 32 − 20 = 12 km/h → option (a)

Why the others are wrong

• (b)
  10 km/h — 20 + 10 = 30 km/h covers only 75 km in 2.5 hours (30 × 2.5), leaving 5 km of the 80 km route still to ride.
• (c)
  15 km/h — 20 + 15 = 35 km/h is too fast: 35 × 2.5 = 87.5 km, more than the 80 km route, so the trip would take under 2.5 hours.
• (d)
  8 km/h — 20 + 8 = 28 km/h is too slow: 80 ÷ 28 ≈ 2.86 hours, so the cyclist still misses the 2.5-hour target.

For a fixed distance, speed and time are inversely proportional: their product is always the distance.

So the time ratio 4 : 2.5 = 8 : 5 flips into the speed ratio 5 : 8, and the new speed is 20 × 8⁄5 = 32 km/h. The question asks for the increase, so subtract the old speed: 32 − 20 = 12 km/h.

Key facts

• Distance = speed × time, so 20 km/h for 4 hours covers 80 km.
• At a fixed distance, speed ∝ 1⁄time: cutting the time from 4 h to 2.5 h multiplies the speed by 4⁄2.5 = 1.6.
• 1.6 times the speed is a 60% increase: 20 km/h → 32 km/h.

Common traps

• Stopping at the new speed, 32 km/h: the question asks by how much the speed must rise.
• Scaling the speed by the time ratio the wrong way round: 20 × 2.5⁄4 = 12.5 km/h is slower, not faster.

No directly related past PYQ was found.