Question

Please solve my question as soon as possible

Answer 1

Question:

Walking at 5/6th of his usual speed , Raman reached his destination 10mins late. Find his usual time .

Answer:

Usual time = 50 mins

Note:

Distance = Speed•Time

Solution:

Let the usual speed of Raman be x units/min and the usual time taken to reach his destination be t mins .

Thus,

=>[The distance travelled by Raman to reach his destination = (Usual speed)•(Usual time)

=> Distance = xt units ------(1)

Now,

According to the question;

If Raman's speed was 5/6th of his usual speed, then he reached his destination 10 mins late.

ie; Raman took 10 mins more to reach his destination.

Thus;

Speed = 5x/6 units/min

Time = (t+10) mins

Also;

=> Distance = Speed × Time

=> Distance = (5x/6)•(t+10)

=> xt = 5x•(t+10)/6 { using eq-1 }

=> xt•6 = 5x•(t+10)

=> 6xt = 5xt + 50x

=> 6xt - 5xt = 50x

=> xt = 50x

=> xt - 50x = 0

=> x(t - 50) = 0

Here ,

Two cases arises.

Case1 : when x = 0

Case2 : when (t - 50) = 0

Case1 :

=> x = 0

This is not possible, because If the speed of Raman become zero , then he would not have reached his destination.

Case2 :

=> t - 50 = 0

=> t = 50

This is appropriate condition.

Hence,

The usual time taken by Raman to reach his destination is 50 mins .