Question

Pankaj was travelling to point B from point A with speed of 45 km/hr. After 1 hour, Pratik also started to travel from point A to point B. Pratik reached the point B 30 minutes before Pankaj. If Pratik would have decreased his speed by 6 km/hr then both would have reached point B at the same time. Find the original speed of Pratik. ​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

60

Step-by-step explanation:

Let the original time taken by Pankaj to reach point B from point A = x hours

Then, the original time taken by Pratik to reach point B from point A = (x−1.5) hours

Also

Let the original speed of Pratik = y km/h

As given, if Pratik would have decreased his speed by 6 km/hr then both would have reached point B at the same time.

Then,

y × (x − 1.5) = (y − 6) × (x−1)

⇒ y × (x − 1.5) = (y − 6) × (x−1)

yx − 1.5y = yx − 6x − y + 6

0.5y = 6x − 6

y = 12x − 12 ....(i)

So, 45 × x = y × (x − 1.5)

From equation (i), we get

45 × x = (12x−12) × (x−1.5)

⇒ 45x = 12x2 − 12x − 18x + 18

⇒ 12x2 − 75x + 18 = 0

⇒ 4x2 − 25x + 6 = 0

⇒ 4x2 − 24x − x + 6 = 0

⇒ 4x(x−6)−1(x−6) = 0

⇒ (4x−1)(x−6)=0

⇒ x = 1/4, 6

Since,

x = 14 is not possible.

So, x = 6

Therefore, the speed of Pratik = y

⇒ 12x − 12 = 60 km/hr