Question

Nikhilesh has to cover 6 km distance. But after travelling 1/3rd distance he gets
tired so he reduces his speed to 3/4th. Again, he covers the same distance and
further reduces his speed to 1/2nd of the reduced speed and reaches 30 minutes
late. What is the usual speed of Nikhilesh?​

Answer 1

Given :- Nikhilesh has to cover 6 km distance. But after travelling 1/3rd distance he gets tired so he reduces his speed to 3/4th. Again, he covers the same distance and further reduces his speed to 1/2nd of the reduced speed and reaches 30 minutes late. What is the usual speed of Nikhilesh ?

Solution :-

Let us assume that, usual speed of Nikhilesh is x km/h .

so,

→ Total distance covered = 6 km

→ Time taken = Distance / speed = (6/x) hours .

now,

→ (1/3) distance = 6 * (1/3) = 2 km

→ Speed = (3/4) of usual speed = (3x/4) km/h .

then,

→ Time taken = D/S = 2/(3x/4) = (8/3x) hours .

and,

→ Next distance covered = 2 km

→ speed = (1/2) of (3x/4) = (3x/8) km/h

then,

→ speed = D/S = 2/(3x/8) = (16/3x) hours.

A/q,

→ 2km at x km/h + 2km at (3x/4) km/h + 2km at (3x/8) km/h = Total time at x km/h + 30 minutes .

→ (2/x) + (8/3x) + (16/3x) = (6/x) + (1/2)

→ (6 + 8 + 16)/3x = (12 + x)/2x

→ (30/3x) = (12 + x)/2x

→ 10 * 2 = 12 + x

→ 20 = 12 + x

→ x = 20 - 12

→ x = 8km/h (Ans.)

Hence, the usual speed of Nikhilesh is 8km/h .

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