Latest CAT Aptitude Question SOLUTION: If a train runs at 40 km/h, it reaches the destination late by 11 mins. But if it runs at 50 km/h, it is late by 5 mins only. The correct time for the train to complete its journey

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(#M40010654) CAT Numerical Ability question Time and Distance Keep an EYE

If a train runs at 40 km/h, it reaches the destination late by 11 mins. But if it runs at 50 km/h, it is late by 5 mins only. The correct time for the train to complete its journey is ?
a) 15 mins b) 21 mins c) 13 mins d) 19 mins.

Asked In CAT Gurpreet S Chohan (11 years ago)

Unsolved Read Solution (11)

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Read Solution (11) :

SDeep Bhattacharya  (11 years ago)

@ ALL :

EXTREMELY SORRY FOR A VERY IDIOTIC SILLY MISTAKE I'VE MADE IN MY POSTED SOLUTION :

At the last step :

we have got

x = (44-25)=19..

[but in my previously posted solution I have miscalculated the subtraction and
produced a stupid result = 21]

So, 19 minutes are taken..

So , the CORRECT ANSWER IS OPTION : d) 19 mins.

Is this solution Helpfull? Yes (12) | No   

Gurpreet S Chohan  (11 years ago)

Let the correct time taken by the train to complete its journey be t mins.
Then, the given situation can be representedas:
Speed (km per hour) 40 50
Time (min) (t + 11) (t + 5) Respectively.

It can be seen that, increase in the speed decreases the time taken.
Therefore, the two quantities are inversely proportional.
40(t + 11) = 50(t + 5)
40t + 440 = 50t + 250
50t – 40t = 440 – 250
10t = 190
t = 19
Thus, the correct time for the train to complete its journey is 19 mins.

Is this solution Helpfull? Yes (9) | No (2)  

SDeep Bhattacharya  (11 years ago)

let x min. is the correct time taken.
d km is the
x+11= d/(40/60)........[EQN(1)]
x+5=d/(50/60)..........[EQN(2)]
Now,
{[EQN(1)]/[EQN(2)] } gives,
(x+11)/(x+5) = (50/60)/(40/60)
=>(x+11)/(x+5) = (5/4)
=>4x + 44 = 5x +25
=> x = (44-25)=21

So, 21 minutes are taken.

Correct Answer is OPTION b)21 mins

Is this solution Helpfull? Yes (6) | No (5)  

Gurpreet S Chohan  (11 years ago)

Let the distance travelled by the train is x kms.
Then, x/40*1000/60 - x/50*1000/60 = 60

=> 60x /40000 - 60x/50000 = 6
=> 60/10000(x/4-x/5) = 6/1
=> x/20=1000
=> x = 20 km

Thus correct time = 20/40 * 60 - 11
= 30 - 11
= 19 mins.

Anyone has a simpler solution ? Help me out

Is this solution Helpfull? Yes (3) | No (3)  

raj kumar  (11 years ago)

ANS: d) 19 mins
Solution:
s=D/T
1. 40=D/(x+11)
2. 50=D/(x+5)
from 1
40x+440=D
from 2
50x+250=D
By solving this two equations, we get x=19 mins

Is this solution Helpfull? Yes (3) | No (1)  

prabhat gupta  (11 years ago)

ans. 19 mins...
soln:
let x is time taken.
x+11= d/50
x+5=d/40
solving these eqn, we get x=19

Is this solution Helpfull? Yes (1) | No (2)  

saikat biswas  (11 years ago)

if the correct time is x, then....
(x+11)*40=(x+5)*50
=>4x+44=5x+25
=>x=19
so,the ans will be 19mins.

Is this solution Helpfull? Yes (1) | No   

prabhat gupta  (11 years ago)

ans. 21 mins...
soln:
let x is time taken.
x+11= d/50
x+5=d/40
solving these eqn, we get x=21...

Is this solution Helpfull? Yes | No (5)  

surendra singh  (11 years ago)

x=40(t-11).....eq(1)
x=50(t-5)......eq(2)
eq(1)=eq(2)
than,t=19
ans(D)
by vikash saini

Is this solution Helpfull? Yes | No   

Chirag Ranjan Lahiri  (9 years ago)

let x is time taken.
x+11= d/50
x+5=d/40
solving these eqn, we get x=19

Is this solution Helpfull? Yes | No   

charan  (6 years ago)

40(t+11)=50(t+5)
t=19 min

Is this solution Helpfull? Yes | No   

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