Please solve these quants questions

[nutz83]

Please do solve this in detail...I have no clue abt races

Ram and Shyam run a race of 2000m.first ram gives shyam a start of 200 m and beats him by 30 s.Next, ram gives Shyam a start of 3 mins and is beaten by 1000 metres.Find the time in minutes in which Ram and Shyam can run the race separately.

Ans : 4 mins and 5 mins

By the way , isn't it unlikely a calender problem will come again?? ...since it came last year...

thanks

[GauravShah]

Originally Posted by nutz83 @ Sat Nov 13, 2004 8:56 am

Please do solve this in detail...I have no clue abt races

Ram and Shyam run a race of 2000m.first ram gives shyam a start of 200 m and beats him by 30 s.Next, ram gives Shyam a start of 3 mins and is beaten by 1000 metres.Find the time in minutes in which Ram and Shyam can run the race separately.

Ans : 4 mins and 5 mins

By the way , isn't it unlikely a calender problem will come again?? ...since it came last year...

thanks

I m using simple time-speed-distance relationships to solve this one...
Shud state that i m usually apprehensive taking up such prob. in the actual test..

Here is wat we can interpret from the two races...

1) In the first race Shyam gets 200 m start... i.e. he has to run only 1800m..

So (Time taken by Ram to run 2000m) = (Time taken by Shyam to run 1800m) - 30
Let speeds be R and S, therefore the equation becomes..
(2000/R) = (1800/S) - 30

2) Ram starts 3 mins after Shyam and losed by 1000m

Hence (Time taken by Ram to run 1000m) = (Time taken by Shyam to run 2000m) - 180
i.e. (1000/R) = (2000/S) - 180

Now solving this for (1/R) and (1/S)...we have
R = (25/3) and S = (20/3)

To find time taken....
For Ram = (2000/R) = 240 = 4 min.
For Shyam = (2000/S) = 300 = 5 min.

Hope i m clear...

Gaurav.

[nutz83]

Hey thanks a lot,Gaurav.You made it very clear.could you also solve this one for me...I tried it along the same lines as the previous one,but couldn't solve it .

In a 100m race ,Shyam runs at 10/6 m/sec.In Shyam gives Sujit a start of 4m and still beats him by 12 seconds what is sujits speed??

Ans: 1.33m/sec


Please tell me when you use this formula :

winners time losers time beat time +start time
-------------- =------------------- = -------------------------------
losers dist winners dist beat dist + start dist

I don't know how to use it in both the problems.

Isn't there also something like beat distance = Losers speed * Beat time

Does this apply in the above case where there is both a beat time and start time....where we could add the beat time and start time for a single beat time?

I hope I'm making my doubts clear

[GauravShah]

Originally Posted by nutz83 @ Sat Nov 13, 2004 11:32 am

Hey thanks a lot,Gaurav.You made it very clear.could you also solve this one for me...I tried it along the same lines as the previous one,but couldn't solve it * .

In a 100m race ,Shyam runs at 10/6 m/sec.In Shyam gives Sujit a start of 4m and still beats him by 12 seconds what is sujits speed??

Ans: 1.33m/sec

On the same lines as the prev prob.....

Time for which Shyam runs = (100m) / (10/6 m/s) = 60 secs....

Now Sujit is given a start of 4m..so he has to run only 96m...and he loses by 12 secs i.e he takes (60+12) secs..

Therefore his speed is (96/72) = 1.33 m/s

Regarding your doubts....I aint very good at using those formlas to solve these problems but will try to explain them a bit later...

Gaurav.

[pendyal]

Originally Posted by rohit_anand @ Wed Nov 10, 2004 5:49 pm

just got a small query...
we always take roots in pairs
as in if we know that 2+root(3) is a root then we assume that 2-root(3) will be a root.
but isn't this true only for equations with rational coefficients?
say if i have an equation
(x-3)(x-2+root(3))=0
then *2+root(3) is not a root even tho 2- root(3) is one...
so what shud be the right approach?...
isnt the assumption that coefficients will be rational wrong?
plz reply
rohit

I had a similar doubt too.
was advised by seniors not to assume that the coefficients are rational unless it is mentioned if such a question comes in the CAT.
you were absolutely right.the irrational roots always occur in pairs only if the coefficients are rational or are rational multiples of the same irrational number.
we have a similar result in complex numbers too.
if a quadratic equation has complex roots then the two roots will always be conjugates of each other or in other words they will always occur in pairs IF AND ONLY IF the coefficients are real.

[vahgar]

1)How to calculate the the no of numbers's between 2 nos:

1) inclusive
2)exclusive
3) between

2) Whats the importance of Circumcenter all I know..just 2/3 of altitude? It seems to come frequently I dont get it..

[newguy]

Originally Posted by vahgar @ Tue Nov 16, 2004 11:06 pm

1)How to calculate the the no of numbers's between 2 nos:

1) inclusive
2)exclusive
3) between

I presume you are asking for the integers between two integers a and b
Inclusive : b-a+1
Exclusive : b-a-1
between : ~ is same as exclusive

2) Whats the importance of Circumcenter all I know..just 2/3 of altitude? It seems to come frequently I dont get it..[/quote]

For an equilateral triangle, circumradius is twice the inradius

there are some formaulae for relating area with the circumradius..check in any book..can't recall now !

[vahgar]

thanks newguy!

[naren_aumech]

Originally Posted by vahgar @ Tue Nov 16, 2004 11:06 pm

2) Whats the importance of Circumcenter all I know..just 2/3 of altitude? It seems to come frequently I dont get it..

As far as I know, the circumcenter is not 2/3 of altitude, but 2/3 of the median....
But I'm not sure.... Anyone can help me out?.....

Naren.

[GauravShah]

Originally Posted by naren_aumech @ Fri Nov 19, 2004 10:42 am

As far as I know, the circumcenter is not 2/3 of altitude, but 2/3 of the median....
But I'm not sure.... Anyone can help me out?.....

Naren.

The circumradius is both 2/3 of the altitude and the median in a equilateral triangle only *. ( Also in an isoceles trianle, only for one of its altitude/median )

In other cases its 2/3 of nothing... ...i mean it wud be 2/3 of something..but i don't know wat that something is...

Correct me if i m wrong guys.

Gaurav.