Official Quant thread for CAT 2013

@sujamait said:
There is a park which is in the shape of a right-angled triangle. A tower is situated at the mid-point of the largestedge of the park. The two perpendicular edges of the park subtend angles of 60์งธand 90์งธ at the top of the tower.Area of the park is 2592*root(2) m^2.What is the height of the tower?A. 72 2 mB. 36 2 mC. 36 mD. 72 mE. None of

Sir, edges subtend angles ka matlab samajh ni aya ๐Ÿ˜ž Aur wo bhi 90 deg??

without stoppage,a train travels at an average speed of 75km/h,with stoppages it covers the same distance at an average speed of 60 km/h.how many minutes per hour does the train stop.

I didn't understand what the question meant.How to solve this ?

@nole 12?
@nole said:
without stoppage,a train travels at an average speed of 75km/h,with stoppages it covers the same distance at an average speed of 60 km/h.how many minutes per hour does the train stop.I didn't understand what the question meant.How to solve this ?
Let the distance be 300 kms
In the 1st case it took 4 hrs
In the 2nd case it took 5 hrs
Difference = 60 mins
Mins / hr=60/5=12 mins
@nole said:
without stoppage,a train travels at an average speed of 75km/h,with stoppages it covers the same distance at an average speed of 60 km/h.how many minutes per hour does the train stop.I didn't understand what the question meant.How to solve this ?
Suppose the distance is 300km....Now with 75km/hr as the speed, it takes 4 hrs to reach destination..

Now due to stopping at diff points in between the journey, av speed reduces to 60km/hr and it takes 5hrs to reach destination.

Hence 1hr stoppage per 5 hrs journey....
Hence 0.2 hr (12 min) stoppage per hour

@nole said:
without stoppage,a train travels at an average speed of 75km/h,with stoppages it covers the same distance at an average speed of 60 km/h.how many minutes per hour does the train stop.I didn't understand what the question meant.How to solve this ?
First Case: 75 kms in 1 hour
Second Case: 60 kms in 1 hour = 75 kms in 1.25 hour = 75 kms in 5/4 hour

Hence Stoppage time of 1/4 hour for every 5/4 hour of journey
That is Stoppage time of 1 hour for every 5 hours of journey = 12 minutes
@nole said:
without stoppage,a train travels at an average speed of 75km/h,with stoppages it covers the same distance at an average speed of 60 km/h.how many minutes per hour does the train stop.I didn't understand what the question meant.How to solve this ?
Suppose -
T=Non-Stoppage time
t=Stoppage time

D / T = 75

D / T + t = 60


Using the equations -

15T = 60t

T/t = 4/1

=> Thus, 12 minutes ?


@nole said:
without stoppage,a train travels at an average speed of 75km/h,with stoppages it covers the same distance at an average speed of 60 km/h.how many minutes per hour does the train stop.I didn't understand what the question meant.How to solve this ?
With stoppages it will cover 60 km in 1 hr or in 60 min
Without stoppages it covers 75 km in 1 hr or 60km in 60/75 or in 48 min.
So it does stop for 12 min in an hour.
@gs4890
@audiq7 yeah its 12 minutes.
A boat sails downstream from point A to point B which is 10 km from A and then returns to A .If the actual speed of the boat is 3km/h,the trip from A to B takes 8 hours less than trip from B to A.What must be the actual speed of the boat for the trip from A to B to take exactly 100 minutes.

I did it like this
stream- x km/h

10/(x+3) +8 = 10/(x-3)

then after getting x,

i substituted in 10(3+x) = 100/60 but not getting the answer.Where did i go wrong?

answer is 4km/h



@nole said:
A boat sails downstream from point A to point B which is 10 km from A and then returns to A .If the actual speed of the boat is 3km/h,the trip from A to B takes 8 hours less than trip from B to A.What must be the actual speed of the boat for the trip from A to B to take exactly 100 minutes.I did it like this stream- x km/h10/(x+3) +8 = 10/(x-3)then after getting x,i substituted in 10(3+x) = 100/60 but not getting the answer.Where did i go wrong?answer is 4km/h
(10/(3-x))-(10/(3+x))=8 where x is speed of stream.
x=2;
from question
10/(2+y) = 100/60, y is speed of boat
y=4

@nole said:
A boat sails downstream from point A to point B which is 10 km from A and then returns to A .If the actual speed of the boat is 3km/h,the trip from A to B takes 8 hours less than trip from B to A.What must be the actual speed of the boat for the trip from A to B to take exactly 100 minutes.I did it like this stream- x km/h10/(x+3) +8 = 10/(x-3)then after getting x,i substituted in 10(3+x) = 100/60 but not getting the answer.Where did i go wrong?answer is 4km/h
Taking speed of boat greater than speed of stream we get the answer but if we take speed of stream greater than speed of boat we don't get the answer matching answer

10/(3+x) + 8 = 10/(3-x)
x = 2

100/60 = 10/(2+x')
x' = 4 ..
@Torque024
@ScareCrow28
ya that is my doubt also.i mean what should i take to be greater quantity speed of boat or speed of stream ?
@ScareCrow28 said:
Taking speed of boat greater than speed of stream we get the answer but if we take speed of stream greater than speed of boat we don't get the answer matching answer 10/(3+x) + 8 = 10/(3-x)x = 2100/60 = 10/(2+x')x' = 4 ..
If speed of stream would be greater than that of boat, then trip from B to A(Upstream) will not be possible.
@Torque024 said:
If speed of stream would be greater than that of boat, then trip from B to A(Upstream) will not be possible.
Common Sense ๐Ÿ˜› .. (Which I missed) ๐Ÿ˜› ..
@deedeedudu said:
Sir 2nd angle 90 hi hai?
@ScareCrow28 said:
Sir, edges subtend angles ka matlab samajh ni aya Aur wo bhi 90 deg??
Q is correct.and it is 90 degrees only..
angle subtended by the edge...means..taking the endpoints of edge and joining with top of pole..the the angle between these to lines is ...90 or 30 as per the case..
I guess now you can proceed.
@deedeedudu said:
B. 10
5 rt3
@sujamait said:
Q is correct.and it is 90 degrees only..angle subtended by the edge...means..taking the endpoints of edge and joining with top of pole..the the angle between these to lines is ...90 or 30 as per the case..I guess now you can proceed.5 rt3
Ohhh achha achha sir! ๐Ÿ˜ƒ samajh agaya
@pari19O1 said:
ye kaise aaya??mera toh 4*(4-rt(3)) aa rha hai...
Since a tangent makes 90 degree with the radius. In the figure the side BC is at roght angle with AO, now the right triangle is formed, i.e BAD, taking AO meets BC at D...
The hypo is 8, perpendicular is 6, hence the base comes out to be 2 root...
but BC= 2* base= 4 root 7
Hope you got the solution...
@tani90 said:
Since a tangent makes 90 degree with the radius. In the figure the side BC is at roght angle with AO, now the right triangle is formed, i.e BAD, taking AO meets BC at D...The hypo is 8, perpendicular is 6, hence the base comes out to be 2 root...but BC= 2* base= 4 root 7Hope you got the solution...
Haan ye toh theek hai...

thanks....

par if u draw the perpendicular to AC or AB and then taking 4 as hypotenuse(OA) and 2 as a side(OE) find the other side...it comes out to be rt(12)....say AE...

EC = 8-rt(12)
BC = 2*EC since two tangents to a circle from a point are of equal length??

isme kya galat hai??

Hope u are getting what i mean??
:)


@pari19O1 Half of this is correct, but half is wrong... :(
See, you said EC= 8- root 12, now EC = the tangent till the point O strikes a perpendicular on BC, if you take that point as D, then EC=CD....
But, you can't surely say that BD would be equal to CD or not.... The remaining value might differ....

Is that fine ? :)