Time speed, work, Alligations and mixtures problems

[catdog]

Originally Posted by hitman

thanx mate.
its a gud approach.
but regardin this qn i still have a doubt .
actually i checked by puttin few values for x.
x=3 y=-1/7 ( as rightly pointed by you , its the max value of f(x) when f(x) is -ve )
x=6 y=1/2
x=7 y=1/9
similarly for higher values of x, y keeps on decreasing. ie y< 1/2 for x>6
so can we say the max value is 1/2.
plz help me out . i'm really confused.

Hi hitman ...c u can write this f(x)=1/x^2-6x+2 as f(x)=1/(x-3)^2-7.............now f(x) will reach to infinity when x-3 will b close to root(7).........x=3+root(7)=5.645.......so just try putting values of x between 5.5 and 6 and u will find max in this range for e.g at 5.7 value of f(x)=3.444 at x=5.65 it is 44.44444 and so on ........its not necessary that f(x) is max at x=infinity


Hope that helps !!!!!!!!!!

[ankursanghi]

Originally Posted by rama_1978

Hi Friends,

This is a problem I came across and was wondering if my approach is correct. Sorry I dont know the correct answer to this one.

Problem:
For every 9 leaps of a rabbit, a hound takes 4 leaps. In each leap the rabbit covers 1 meter while the hound covers 2+1/3 meters. In how many leaps would the hound catch the rabbit if the rabbit has a start of 16 meters.

Options:
1. 172
2. 152
3. 192
4. None of these.

My reasoning:
In 9 leaps the rabbit covers 9 meters. In 4 leaps the hound covers 9+1/3 meters. Thus the difference is 1/3 meters.
Therefore, number of leaps = 16x4/(1/3)= 16x3x4 = 192 leaps.

Could anyone please tell me if my logic and answer is correct?

Thanks,
-Rama.

You are correct!! I find no flaw in your reasoning.

[eagles_dare13]

where in ptindia can we find brain teasers..?
pls help

[eagles_dare13]

thanx min max.....i got that..

as yur name shows, no one can beat yu in maxima minima probs )

carry on !

Originally Posted by catdog

Hi eagle


i think differentiation method will also work fine but u shud differentiate 1/(x^2-6x+2) to get the correct answer .........if u approachis that if g(x)=1/f(x)...then at min(f(x) we shud get max(g(x))....is not correct since this is applicable only if f(x) and g(x) both assume +ve values only ..............hope that helps!!!!!!!!

[minali]

in 9 leaps rabbit covers 9 m n the hound covers (2+1/3)m
so the hound has a lead by 1/3 m in 4 leaps
or a lead of 1/12 per leap
thus , 1/12 .x =16
or x= 16 *12 =192


where x is the no of leaps

Originally Posted by rama_1978

Hi Friends,

This is a problem I came across and was wondering if my approach is correct. Sorry I dont know the correct answer to this one.

Problem:
For every 9 leaps of a rabbit, a hound takes 4 leaps. In each leap the rabbit covers 1 meter while the hound covers 2+1/3 meters. In how many leaps would the hound catch the rabbit if the rabbit has a start of 16 meters.

Options:
1. 172
2. 152
3. 192
4. None of these.

My reasoning:
In 9 leaps the rabbit covers 9 meters. In 4 leaps the hound covers 9+1/3 meters. Thus the difference is 1/3 meters.
Therefore, number of leaps = 16x4/(1/3)= 16x3x4 = 192 leaps.

Could anyone please tell me if my logic and answer is correct?

Thanks,
-Rama.

[catdog]

Originally Posted by MrAnderson

61* 94 and 92 * 65 ..
y dont u compare ..61/65 and 92/94
61/65 is 1-(4/65) and the other is 1- (2/94)
clearly... 92/94 is bigger => 92 * 65 is greater..
cos if a/b > c/d then ad > bc...
just a thot...
andy.

i think it is better to multiply rather than doin all this ...anyways nice thuts ..........

Here s what i suggest

61*94=(65-4)*94=65*94-94*4

92*65=65*(94-2)=65*94-65*2.........

Now u can easily tell which is greater

[ckartik]

Originally Posted by rama_1978

Hi Friends,

This is a problem I came across and was wondering if my approach is correct. Sorry I dont know the correct answer to this one.

Problem:
For every 9 leaps of a rabbit, a hound takes 4 leaps. In each leap the rabbit covers 1 meter while the hound covers 2+1/3 meters. In how many leaps would the hound catch the rabbit if the rabbit has a start of 16 meters.

Options:
1. 172
2. 152
3. 192
4. None of these.

My reasoning:
In 9 leaps the rabbit covers 9 meters. In 4 leaps the hound covers 9+1/3 meters. Thus the difference is 1/3 meters.
Therefore, number of leaps = 16x4/(1/3)= 16x3x4 = 192 leaps.

Could anyone please tell me if my logic and answer is correct?

Thanks,
-Rama.

Dude
I m getting 185 as the answer .Plz check if theres any flaw.....


Let speed of rabbit be 9mpt and that of hound be 28/3 mpt

relative speed be 1/3 mpt

The 'difference distance' is 16 m

there fore the time taken is 48 t
in this time rabbit travels a distance of 48*9m

7/3 m - 1 leaps for the hound
48*9 m ??
= 48*9*3/7
=185.1428m

[catdog]

Originally Posted by ckartik

Dude
I m getting 185 as the answer .Plz check if theres any flaw.....


Let speed of rabbit be 9mpt and that of hound be 28/3 mpt

relative speed be 1/3 mpt

The 'difference distance' is 16 m

there fore the time taken is 48 t
in this time rabbit travels a distance of 48*9m

7/3 m - 1 leaps for the hound
48*9 m ??
= 48*9*3/7
=185.1428m

I think u made a mistake after calculating 48t

Total time elapsed = 48t

Hound makes 4 leaps in 1 t

therefor he will make 4*48=192 leaps in 48 t

Mistake u made is that u assumed hound will also travel 48*9 meters which not correct Hound will travel 48*9+16 meters now u will get ur answer .........

[shivasmiles]

Hey Guys there


Need a very simple and logical solution for this without formulae...
I have done with a formula but without that




In a village which has a barter system, 1 kg of sugar is equivalent to one dozen mangoes.
'A' gives 1.5 kg sugar to 'B' using a false weight of 800 gm as 1 kg and takes 15 mangoes.
Who is in profit and what is the percentage profit?

1) 8.34% to 'A' 2) 8.34% to 'B' 3) 4.17% to 'A' 4) Cannot be determined




Shiva

[estranged_gnrs]

Originally Posted by shivasmiles

Hey Guys there


Need a very simple and logical solution for this without formulae...
I have done with a formula but without that




In a village which has a barter system, 1 kg of sugar is equivalent to one dozen mangoes.
'A' gives 1.5 kg sugar to 'B' using a false weight of 800 gm as 1 kg and takes 15 mangoes.
Who is in profit and what is the percentage profit?

1) 8.34% to 'A' 2) 8.34% to 'B' 3) 4.17% to 'A' 4) Cannot be determined




Shiva

answer is 3) 4.17 to A

its mental calc. u can see that A actually sold 1.2 kg sugar,so he shld have got 14.4 mangoes,but he got 15 mangoes.so profit of 0.6,which is 4.17 % of 12.

Rohit