The distance of the college and the home of Rajeev is 80 km. One day was late by 1 h than the normal time to leave for the college, so he increased his speed by 4 km/h and thus he reached to college at the normal time. What is the changed (or increased) speed of Rajeev?a)28 km/hb)30 km/hc)40 km/hd)20 km/hCorrect answer is option 'D'. Can you explain this answer?

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The distance of the college and the home of Rajeev is 80 km. One day was late by 1 h than the normal time to leave for the college, so he increased his speed by 4 km/h and thus he reached to college at the normal time. What is the changed (or increased) speed of Rajeev?

a)
28 km/h
b)
30 km/h
c)
40 km/h
d)
20 km/h

Correct answer is option 'D'. Can you explain this answer?

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The distance of the college and the home of Rajeev is 80 km. One day w...

Let the normal speed be xkm/h, then

x(x+20)−16(x+20)=0 ⇒ (x+20)(x−16)=0 ⇒ sx=16km/h ∴ (x+4)=20km/h Therefore, increased speed = 20 km/h

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The distance of the college and the home of Rajeev is 80 km. One day w...

Given information:
Distance between Rajeev's home and college = 80 km
Let the normal speed of Rajeev be x km/h
He was late by 1 hour, so he increased his speed by 4 km/h and reached the college at normal time.

To find: Changed (or increased) speed of Rajeev

Calculation:
Let's assume that the normal time taken by Rajeev to travel from home to college is T hours.
So, according to the given information, Rajeev was late by 1 hour, which means he took T+1 hours to reach the college.

Using the formula of speed, distance, and time:
Normal speed = distance/time = 80/T km/h
Increased speed = normal speed + 4 = (80/T) + 4 km/h

Now, we know that Rajeev reached the college at normal time, which means he took the same time T to travel from home to college at an increased speed.

Using the formula of speed, distance, and time:
Increased speed = distance/time = 80/T km/h

Equating the above two equations, we get:
(80/T) + 4 = 80/T

On solving this equation, we get:
T = 5 hours

Substituting the value of T in the equation of increased speed, we get:
Increased speed = 80/T = 16 km/h

Therefore, the changed (or increased) speed of Rajeev is 16 km/h, which is option (d).

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