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Koustav Pal
@allan89
5,965

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

IIM Kozhikode PGP 2014-16| CAT'13 99.43 | XAT'14 97.21 http://www.pagalguy.com/discussions/all-i-wanted-to-speak-about-cat-25002933/19890122

udit pande
@upudit0
1,640

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

option 2)

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Thilak Kumar
@HydRocker
4,274

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

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Jai Mehra
@jaikishan.n
1,520

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

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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Saransh Sood
@Enceladus
7,341

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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Abhishek Jain
@jain4444
40,426

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

- 1 Like

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Thilak Kumar
@HydRocker
4,274

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

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Koustav Pal
@allan89
5,965

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?

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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Saransh Sood
@Enceladus
7,341

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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Koustav Pal
@allan89
5,965

==========================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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@speedyshoeb
12

=> Copper= around 25.2 kg

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wrong post..............

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Thilak Kumar
@HydRocker
4,274

(1) 5:15 a.m. (2) 5:30 a.m.

(3) 6:00 a.m. (4) 5:45 a.m.

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