help needed for the questions below

Hi All,

Can you please provide me the solutions to the below problems with steps on how to get the answer for the question below.

I know the below problem is related to HCF or LCM but i am finding it difficult to implement the concept to get to the solution.

At a book store ,MODERN BOOK STORE,is flashed using neon light.The word is individually flashed at interval 5/2,17/4,41/8 seconds respectively ,and each word is put off after a second.The least time after which the full name of the book store can be read again is?

A red light flashes 3times per min and green light 5times in 2mins at regular interval.If both light flashing at the same time,how many time do they flash together in each hour.

This is a different problem.

A train approaches tunnel AB.Inside the tunnel is a cat located at point 3/8th of the distance AB measured from the entrance A.When the train whistles the cat runs.If the cat moves to the entrance of the tunnel A the train catches the cat exactly at the entrance.If the cat moves to the exit ,the train catches the cat at exactly the exit,B,the speed of the train is greater than the speed of the cat by what order?

I want the steps and explanation on how you arrived at solution please.

Thanks.

3 Attachment(s)

Re: help needed for the questions below

First, congratulations on your English. I am much more likely to answer questions that are written clearly and in good English. There are three attachments as my answer.

Attachment 26625

Attachment 26626

Attachment 26627

Re: help needed for the questions below

Hi ,

Thanks for the lightning response john.

For the answer of the second question i did not quite understand the following.

So at 2mins the red light comes on for the 6th time

and the green light comes on for the 5th time

and this is the fist time the lights come togehter.Can you please clarify.Also m and n stands for which of the light.

Thanks.

Re: help needed for the questions below

The red light comes on every 1/3 minute and the green light every 2/5 minute. So:

red light comes on at times 1/3, 2/3, 3/3, 4/3, 5/3, 6/3 and in general m*1/3 for m any positive integer

green light comes on at times 2/5, 4/5, 6/5, 8/5, 10/5 and in general n*2/5 for n any positive integer

I hope it is now clear that the two lights come on at the same time for the first time at 2 minutes.

Re: help needed for the questions below

Sorry but i am still not clear about how the two light come together on at the same time at 2mins.How can u conclude that the two lights come together after 2mins from the above explanation ,sorry but i am not getting it.

Re: help needed for the questions below

Hold a stop watch.

The red light comes on after 20 seconds and then immediately goes off; after 20 more seconds the red light comes on again. So far you have 40 seconds on your stop watch. Continue this for 4 more cycles. Your stop watch reads 120 seconds or 2 minutes.

So the red light comes on at 20, 40, 60, 80, 100, 120 seconds from the start.

Now do the same for the green light.

Green light on after 2/5 minute or 24 seconds, then again at 48 seconds, 72 seconds, etc.

The green light comes on at 24, 48, 72, 96, 120 seconds from the start.

Look at the two sequences. The first time after the start at which both lights are on is 120 seconds.