### Finding The Time Of Arrival

**What was the puzzle?**

Let

**'x'**km/minute be the

**speed**of

**Rohit**'s walk. He started to walk at

**12**PM & met Samit at

**4:05**PM. That means he has walked for

**245**minutes.

Distance traveled by

**Ro**

**hit**=

**245x**km

Let

**'y'**km/minute be the

**speed**of

**Samit**'s walk. He started to walk at

**2**PM & met Samit at

**4:05**PM. That means he has walked for 125 minutes.

Distance traveled by

**Samit**=

**125y**km

Time of Meeting |

Now after meeting each other they resumed their journey further. That means Rohit continues to

**Tumkur**& covers distance of

**125y**km at his speed of

**x**km/minute. Time taken by him further to complete the journey is

**125y / x**minutes (Time = Distance/Speed).

Similarly,

**Samit**need to travel

**245x**km to reach

**Bangalore**at speed of

**y**km/minute. So he took time

**245x / y**minutes to reach the destination.

Since both reached at the same time at their respective destinations after meeting each other at

**4:05**PM, time taken by them to complete rest of journey must be equal.

Hence,

**125y / x = 245 x / y**

245 x^2 = 125 y^2

x^2 / y^2 = 125 / 245 = 25 / 49

**x / y = 5 / 7**

Now, we have ratio of x / y which we can put in 'time' taken by Rohit & Samit.

So Rohit took 125 y / x = 125 * ( 7 / 5) =

**175**minutes to reach Tumkur & obviously Samit required 245 x / y = 245 * ( 5 / 7) =

**175**minutes.

To conclude, after meeting each other at 4:05 PM both reached at their respective destination in 175 minutes =

**2 hours 55 minutes**i.e. at

**7 PM**

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