Time,Speed and Distance

[imgonnacrackthistime]

hey all serious Catties,
I have been scanning PG from over 3 months but I haven't come across any structured thread to Quant questions.I have seen some good questions but there r lying all scattered. and even some has so ambiguities that it puts me off like "I'll post tough questions". and even "Lets crack 2004" has good discussions but has no structured questions. I have thought to post good quality real CAT-like questions topic wise. in this any person posting 2 or 3 good quality questions at a time and posting answers for the same within a day. Today i m starting with TSD. I m posting 2 questions. count on me to post answers of these by 10 pm tomorrow. and also count on me to start other threads. I wud like to summon all serious catties for this.

1. A train approaches a tunnel AB. Inside a tunnel one cat is located at a point that is 3/8th of the distance AB. measured from A.When train whistles , cat runs. .If the cat moves to the entrance of the tunnel AB, train catches cat exactly at the entrance. If the cat moves to exit B, the train catches that cat at the exit B. the speed of the train : speed of the cat
a) 3:1 b) 4:1 c) 5:1 d) none of these

2. A thief is 27 steps away from a police man.the thief takes 8 steps to 5 steps of police man.But 2 steps of police man is same as 5 steps of thief.
can police man catch thief? how many steps officer needs to catch the thief?
a)75 b) 30 c) 50 d) 25

[ankursanghi]

For ques 1.

Say AB is the length of the tunnel. And Train is X distance away from A. Let speed of cat be Sc and speed of Train be St. Now when the Train and Cat meet at A, time taken by cat to cover up 3/8 * AB is equal to time taken by Train to cover X. So, X/St = (3/8 * AB)/Sc. Similarly get an equation for Cat and Train reaching point B.
The answer is b (4:1)

[TheAkshaT]

Originally Posted by imgonnacrackthistime

2. A thief is 27 steps away from a police man.the thief takes 8 steps to 5 steps of police man.But 2 steps of police man is same as 5 steps of thief.
can police man catch thief? how many steps officer needs to catch the thief?
a)75 b) 30 c) 50 d) 25

In time t
5t steps of policeman = 12.5t steps of thief....

so policeman is running 4.5 steps per unit time fater than thief...

27/4.5 = 6 units of time = time taken by policeman to catch him...

thus steps taken by policeman = 5*6 = 30

-Akshat

[haripi2]

Originally Posted by TheAkshaT

In time t
5t steps of policeman = 12.5t steps of thief....

so policeman is running 4.5 steps per unit time fater than thief...

27/4.5 = 6 units of time = time taken by policeman to catch him...

thus steps taken by policeman = 5*6 = 30

-Akshat

akshath i beg to differ..answer seems to be 75..

using the principle of inverse proportions
for every 16 steps (8*2) the thief takes the policeman takes 25 steps(5 * 5)
so policeman gains 9 steps for every 25 steps
to gain 27 steps he would require 25 * 3 = 75 steps.

[urz_mitr]

. A thief is 27 steps away from a police man.the thief takes 8 steps to 5 steps of police man.But 2 steps of police man is same as 5 steps of thief.
can police man catch thief? how many steps officer needs to catch the thief?
a)75 b) 30 c) 50 d) 25


Solution ---------------

1 step of policeman = 2.5 steps of thief

5 steps of PM = 12.5 steps of Th

for every 5 steps of PM Thief run 8 steps

i.e PM is covering 12.5-8 = 4.5 steps of Th => 5 steps of PM covers 4.5 steps of Th betweem them

Thief is 27 steps ahead .... i.e 27 = 4.5x2x3

=> 5x2x3 = 30 steps of PM can catch Thief

[imgonnacrackthistime]

sorry guys i cudn't post the answers yesterday. went to marriage and came late.
answers are-
1. 4:1
2. 30

a
I'l post explnations late in the day . My PL is standing on my head

[imgonnacrackthistime]

hey guys.

1. As cat is standing at 3/8 of AB measured from A. suppose distanse is 8 units..
so when cat runs toward the entry A i.e when it travels 3 units then train reaches the entry A. now When train whistles and cat moves towards the exit
so when train reaches the entry A the cat must have covered 3 units in directions towards B.
Now for train to catch cat at exit B. it must travel 8 units and cat 2 units in same time.
so ratio of speed is 4:1

this is my way
others answers r also correct.
2.
8 steps of thief = 5 steps of police
16 of thief = 10 of police -- (1)
now 2 steps of police = 5 steps of thief

so (1) becomes
16 of thief = 25 of police
diff of 9 steps
and thief is initially 27 steps ahead
so 27/9 =3
therfore 3*25 =75 steps of poilice needed.
but this no of steps are in the form of thief steps.
so 75*2/5= 25
so 25 poice steps needed.

[imgonnacrackthistime]

sorry last one is 30 steps .

[koolfriend4u]

Hii "i'm gonna crack" well. u did smart for the first prob.

but the second one 3 * 25 u did mistake.

its actually 3 * 10 ( 2 times of unit time) = 30
therfor 30 steps of police.

more speed probs i expect from ur side.

[koolfriend4u]

Two cars are headed for Phoenix. One is 50 miles ahead of the other on the same road. The one in front is traveling at 60 mph while the second car is traveling at 70 mph. How long in hours will it take for the second car to overtake the first?