On a 300 km long racing track, three bikes — A, B, and C take part in a race. Initially, their speeds are 50 km/hr for Bike A, 40 km/hr for Bike B, and 60 km/hr for Bike C. After the first 2 hours of racing, their speeds are altered as follows:
Bike A adopts a new speed which is 25% more than Bike C’s speed at that moment.
Bike B increases its speed by 10% compared to its original speed.
Bike C reduces its speed to 80% of Bike A’s original speed.
Find the time gap (in minutes) between the bikes that finished first and second.

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Total distance = 300 km

Initial speeds for first 2 hours:
Bike A = 50 km/hr
Bike B = 40 km/hr
Bike C = 60 km/hr

After 2 hours:

Bike A speed = 125% of Bike C's speed at that time
Bike B speed = 110% of original speed = 44 km/hr

Bike C speed = 80% of Bike A's original speed = 40 km/hr

Distance = Speed × Time

Total time = Time1 (first 2 hours) + Time2 (remaining distance ÷ new speed)

Time gap = Difference between total time taken by 1st and 2nd finisher

Convert time difference to minutes (multiply by 60)

Bike A: 50 × 2 = 100 km

Bike B: 40 × 2 = 80 km

Bike C: 60 × 2 = 120 km

A: 200 km left

B: 220 km left

C: 180 km left

Bike C’s speed after 2 hours = 60 km/hr (unchanged till that moment)

So, Bike A’s new speed = 125% of 60 = 1.25 × 60 = 75 km/hr

Bike B’s new speed = 40 + 10% of 40 = 44 km/hr

Bike C’s new speed = 80% of 50 = 0.8 × 50 = 40 km/hr

Bike A: 200 ÷ 75 = 8/3 hours

Bike B: 220 ÷ 44 = 5 hours

Bike C: 180 ÷ 40 = 4.5 hours

Bike A: 2 + 8/3 = 14/3 hours

Bike B: 2 + 5 = 7 hours

Bike C: 2 + 4.5 = 6.5 hours

Bike A finishes first (14/3 hours)

Bike C finishes second (6.5 hours)

Time gap = 6.5 - $$\frac{14}{3}$$​

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​$$\frac{39 - 28}{6} = \frac{11}{6} \text{ hours}$$​

= $$\frac{11}{6}$$​× 60 = 110 minutes