A student takes 1.5 hours from home to school at a speed of 5 km/h. By what percent should he increase his speed to reduce the time by 20% and cover the same distance from school to home?

Correct option is A

Given:

The student travels at a speed of 5 km/h and takes 1.5 hours.

Time decreases by 20%.

Formula used:

Speed= distance/ time

Solution:

Let the distance from home to school be d kilometers.

The student travels at a speed of 5 km/h and takes 1.5 hours.

The distance is

d =$$\text{speed} \times \text{time} = 5 \times 1.5$$​ = 7.5 km


The student wants to reduce the time by 20%. The reduced time is:

Reduced time = $$1.5 - 0.2 \times 1.5$$​ = 1.5 - 0.3 = 1.2 hours


New speed
Let the new speed be v km/h.

The student will cover the same distance of 7.5 km in 1.2 hours. The new speed can be calculated as:


v =$$\frac{d}{\text{Reduced time}} = \frac{7.5}{1.2}$$​= 6.25 km/h


The original speed is 5 km/h, and the new speed is 6.25 km/h. The percentage increase in speed is given by:

Percentage increase= $$\frac{6.25 - 5}{5} \times 100 = \frac{1.25}{5} \times 100$$​ = 25%


Thus, the student should increase his speed by:25%