In covering a distance of 90 km, Anirudh takes 8 hours more than Burhan. If Anirudh doubles his speed, then he would take 7 hour less than Burhan. Anirudh's speed is:

Given:

Distance = 90 km

Anirudh takes 8 hrs more than Burhan at normal speed

If Anirudh doubles his speed, he takes 7 hrs less than Burhan

Formula used:

Time = Distance ÷ Speed

Calculation:

Burhan's speed = x km/h

Anirudh's speed = y km/h

So, Burhan's time = 90 ÷ x

Anirudh's time = 90 ÷ y

Anirudh's time when speed is doubled = 90 ÷ (2y)

Using condition 1:

⇒ 90 ÷ y = 90 ÷ x + 8 ...(i)

Using condition 2:

⇒ 90 ÷ (2y) = 90 ÷ x − 7 ...(ii)

Multiply (i) by 2:

⇒ 180 ÷ y = 180 ÷ x + 16

Subtract (ii) from this:

(180 ÷ y − 90 ÷ (2y)) = (180 ÷ x + 16) − (90 ÷ x − 7)

⇒ (180 − 90) ÷ (2y) = (180 − 90) ÷ x + (16 + 7)

⇒ 90 ÷ (2y) = 90 ÷ x + 23

Now substitute:

Let’s solve equation (i):

90 ÷ y = 90 ÷ x + 8

⇒ 90 ÷ x = 90 ÷ y − 8

Now use in equation (ii):

⇒ 90 ÷ (2y) = (90 ÷ y − 8) − 7 = 90 ÷ y − 15

⇒ 90 ÷ (2y) = 90 ÷ y − 15

Multiply both sides by 2:

⇒ 90 ÷ y = 180 ÷ y − 30

⇒ 90 ÷ y − 180 ÷ y = −30

⇒ − 90 ÷ y = −30

⇒ y = 3

∴ Anirudh's speed is 3 km/h.