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Official Quant Thread for CAT 2012 [Part 1]

Hi puys, CAT 2011 season is finally over :: :: Let start a new season of Quants thread for CAT 2012.. :: :: Here are few links of Quants thread for CAT 2011 season... Part-8 http://www.pagalguy.com/forum/quanti...at-...
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A 250 m long train is approaching an unmanned railway crossing. The train is
running at a uniform speed of 75 km/h and is 3 km away from the crossing. At the same instant, a scooter is also approaching the crossing and is 1300 m away from it. The scooter is moving at a uniform speed of A. In which of the following ranges, A exists such that the scooter would pass the crossing by just escaping the collision?
(1) 24km/h to 28 km/h
(2) 29km/h to 33km/h
(3) 35km/h to 40km/h
(4) 41km/h to 45km/h
(5) 45 km/h to 50km/h


train___________crossing_________scooter

,-------1.3------------>

total distance between scooter and train=4.3km

time to collide t= 4.3/75+A................1

also t*A=1.3km....................2

using 1&2 we get A=32.5kmph in order to just avoid collision

so A should be in the range 29
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A 250 m long train is approaching an unmanned railway crossing. The train is running at a uniform speed of 75 km/h and is 3 km away from the crossing. At the same instant, a scooter is also approaching the crossing and is 1300 m away from it. The scooter is moving at a uniform speed of A. In which of the following ranges, A exists such that the scooter would pass the crossing by just escaping the collision?
(1) 24km/h to 28 km/h
(2) 29km/h to 33km/h
(3) 35km/h to 40km/h
(4) 41km/h to 45km/h
(5) 45 km/h to 50km/h


sol:
time taken by train =3/75 hr
and time taken by scooter=1.3/A
they will collide if 3/75=1.3/A
A=32.5 km/hr
now for escaping collison A>32.5
option 2)
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A truck having ten tyres travels from P to Q and then back to P. If there are 2 additional spare tyres and the distance between P and Q is 9000 kilometres (km), then the maximum distance travelled (in km) by any tyre is at least?
(1) 12000 (2) 18000 (3) 9000 (4) 16000 (5) 15000

"You are the creator of your own Destiny."
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Ajit, Ashutosh and Anil started from the same place and travelled in the same direction at the speeds of 80, 70 and 60 kmph respectively. Ashutosh started 3 hours after Anil and both Ajit and Ashutosh overtook Anil at 9.00 p.m. of the same day. Find the time at which Ajit started?
(1) 5:15 a.m. (2) 5:30 a.m.
(3) 6:00 a.m. (4) 5:45 a.m.


my take5:15 a.m.
in 3 hours anil would have travelled 180 kms.
effective speed of ashu and anil = 10 kmph

it would take 18 hours for them to cover 180kms gap. so 9:00 p.m. - 18 hours = 3 a.m. was when ashu started and 00:00 was the time when anil started.
so anil travelled for 21 hrs before he met ajit. In 21 hrs anil was 60*21 = 1260kms away from the starting point. Ajit would take 1260/80*60 = 945 minutes before they meet.

945 minutes = 15 hours 45 minutes.
so 9:00 p.m - 15 hours 45 minutes = 5:15 a.m.
  • 1 Like  
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A 250 m long train is approaching an unmanned railway crossing. The train is
running at a uniform speed of 75 km/h and is 3 km away from the crossing. At the same instant, a scooter is also approaching the crossing and is 1300 m away from it. The scooter is moving at a uniform speed of A. In which of the following ranges, A exists such that the scooter would pass the crossing by just escaping the collision?
(1) 24km/h to 28 km/h
(2) 29km/h to 33km/h
(3) 35km/h to 40km/h
(4) 41km/h to 45km/h
(5) 45 km/h to 50km/h


Getting option 2.

The train will cover this 3km in 0.04 hrs.
The scooter needs to cover 1.3 km in less than 0.04 hrs.
=> Speed of scooter = A = 1.3/Time.
=> 1.3/A => A > 1.3/0.04.
So A > 32.5 kmph.
  • 2 Likes  
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kindly solve this question...GUY!!!

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Ajit, Ashutosh and Anil started from the same place and travelled in the same direction at the speeds of 80, 70 and 60 kmph respectively. Ashutosh started 3 hours after Anil and both Ajit and Ashutosh overtook Anil at 9.00 p.m. of the same day. Find the time at which Ajit started?
(1) 5:15 a.m. (2) 5:30 a.m.
(3) 6:00 a.m. (4) 5:45 a.m.


60*3 = 180 km

180/70-60 = 18 hrs

18*70 = 1260 km

1260/80 = 15.75

9:00 pm - 15 hrs 45 mins = 5:15 am = answer
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RC practice :- http://codecoax.com/grerc/
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A 250 m long train is approaching an unmanned railway crossing. The train is
running at a uniform speed of 75 km/h and is 3 km away from the crossing. At the same instant, a scooter is also approaching the crossing and is 1300 m away from it. The scooter is moving at a uniform speed of A. In which of the following ranges, A exists such that the scooter would pass the crossing by just escaping the collision?
(1) 24km/h to 28 km/h
(2) 29km/h to 33km/h
(3) 35km/h to 40km/h
(4) 41km/h to 45km/h
(5) 45 km/h to 50km/h

"You are the creator of your own Destiny."
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997 it will be :thumbsup:



My take is option 2.

f(0) = 0^3 - 4*0 + p = p.
f(1) = 1^2 - 4*1 + p = p - 3.
Since p and p - 3 are of opp signs then p*(p-3) => 0
==========================

Q) An alloy of copper and tin contains 77.78% of copper. After 18kg of tin is added, the copper content gets reduced to 50%. How much copper and tin do the new allow had respectively?

copper 25.2 kg and tin 7.2 kg previously

Approach:-

initial conc of copper=7/9 and tin=2/9

in the quantity i.e 18 kg which is added conc of copper =0%

now, final conc of copper in resulting mixture is 50% =1/2

so using alligation,

we get ratio of quantity in which the 1st alloy and the extra tin added later=9:5

=>5 parts=18kg

=>9parts=162/5kg=32.4[= this is the original volume of the alloy]

=>qty of copper in original alloy= 7/9 * 162/5 =126/5=25.2kg

=>qty of tin in original alloy=32.4kg-25.2kg=7.2kg

in new alloy qty of copper =25.2; qty of tin=18+7.2=25.2kg ;final volume of 2nd alloy=50.4kg
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Ajit, Ashutosh and Anil started from the same place and travelled in the same direction at the speeds of 80, 70 and 60 kmph respectively. Ashutosh started 3 hours after Anil and both Ajit and Ashutosh overtook Anil at 9.00 p.m. of the same day. Find the time at which Ajit started?
(1) 5:15 a.m. (2) 5:30 a.m.
(3) 6:00 a.m. (4) 5:45 a.m.


My take is 5:15 am
Anil covers 180km in 3 hrs.
Ashutosh overtakes Anil in 180/10 = 18 hrs.
Ashutosh in 18 hrs covers = 18*70 = 1260 km.
=> Ajit overtakes Anil in 1260/80 = 15 3/4 hrs
So, Ajit started at 5.15 am.
  • 1 Like  
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==========================

Q) An alloy of copper and tin contains 77.78% of copper. After 18kg of tin is added, the copper content gets reduced to 50%. How much copper and tin do the new allow had respectively?


initial conc of tin= 2/9 and that of copper=7/9

copper 25.2 kg ; tin =7.2 kg previously
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Q) An alloy of copper and tin contains 77.78% of copper. After 18kg of tin is added, the copper content gets reduced to 50%. How much copper and tin do the new allow had respectively?

=> Copper= around 25.2 kg
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wrong post..............

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Ajit, Ashutosh and Anil started from the same place and travelled in the same direction at the speeds of 80, 70 and 60 kmph respectively. Ashutosh started 3 hours after Anil and both Ajit and Ashutosh overtook Anil at 9.00 p.m. of the same day. Find the time at which Ajit started?
(1) 5:15 a.m. (2) 5:30 a.m.
(3) 6:00 a.m. (4) 5:45 a.m.

"You are the creator of your own Destiny."
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