If niti drives her car at 5okm/hr from her home,she reaches the office late by 10min. However if she drives at 60km/hr,she reaches the office 5min early.find the distance of the office from her home.

5 + 10 = 15 min = 0.25 hours.

d1 = d2.
50t = 60(t-.25)
50t = 60t - 15
50t - 60t = -15
-10t = -15
t = 1.5 h.

D = r*t = 50 * 1.5 = 75 Miles.

To find the distance of the office from Niti's home, we can use the formula:

Distance = Speed × Time

Let's consider the time it takes Niti to travel from her home to the office at 50 km/hr. She reaches the office 10 minutes late. We need to convert these minutes into hours by dividing by 60:

10 minutes = 10/60 = 1/6 hours

So, the time taken by Niti to travel at 50 km/hr is: (t + 1/6) hours.

Now, let's consider the time it takes Niti to travel from her home to the office at 60 km/hr. She reaches the office 5 minutes early. Again, we need to convert these minutes into hours:

5 minutes = 5/60 = 1/12 hours

So, the time taken by Niti to travel at 60 km/hr is: (t - 1/12) hours.

We can set up an equation using the formula Distance = Speed × Time for both scenarios:

50(t + 1/6) = 60(t - 1/12)

Now, we can simplify and solve for t:

50t + 50/6 = 60t - 60/12
50t + 50/6 = 60t - 5
50t - 60t = -5 - 50/6
-10t = - (5*6 + 50)/6
-10t = - (30 + 50)/6
-10t = - (80)/6
t = 8/6
t = 4/3 hours

Now, we can find the distance by substituting the value of t into either equation:

Distance = 50(t + 1/6)
Distance = 50(4/3 + 1/6)
Distance = 50(8/6 + 1/6)
Distance = 50(9/6)
Distance = 450/6
Distance = 75 km

Therefore, the distance from Niti's home to the office is 75 km.