Aptitude - Problems on Trains - Discussion

Hey @Prity and @Prem
See
(1) S km/hr = S.5/18 m/sec
(2) S m/sec = S.18/5 km/hr

That's why
50.5/18 -X.5/18 = 220/6 m/sec
250/18 -X.5/18 = 220/6 m/sec
- X.5/18 = 220/6 . 18 /250 m/sec

Now all are in m/ sec but now the game will be changed
Suppose if I move 5/18 from left side to right side so according to second rule m/sec. 18/5 =km/hr

-X = 220/6. 18 /250. (5/18) the value will be in km/hr
After all the calculation you will get the same answer in km/hr.

I hope you got the logic behind it.

220m=0.220km : 6 sec = 1/600 hr.

0.220/ (50+x) = 1/600
0.220x600 = (50+x) => 132 = 50+x

x = 132-50=82,
x=82 km/hr.

The answer is 82 km/h is correct. They have shown calculation for relative speed in wrong way.

Speed for 1st train is 50 km/h after conversion it will be 250/18 m/s.
And suppose speed for the second train in x m/s.
Relative speed will be (125 +9x)/9 m/s.

Then,
(125+9x)/9 = 108+112/6.
750+54x = 1980.
54x = 1230.
x = 22.78 m/s.

After conversion to km/h.
22.78x18/5= 82 km/h. Approx.

I believe this how they should have done.

Here, time is in seconds & distance is in meters that's why we have to convert the speed into m/sec. Initially assume that X is in km/hr. SO we have to convert the speed in m/sec as all parameters is in meter & seconds. After solving where get the value of x in km/hr,

Thanks all for explaining.

Why have we assumed x in km/he why not in m/s?


Please, someone, explain it.

Thanks @Mahi.

Given :
(length of 1st train) L1 = 108 m.
(length of 2nd train) L2 = 112 m.
(speed of 1st train) S1 = 50 KMPH = 50* 5/18 = 250/18.

(time taken to cross each other)T = 6 s.

Solution :
T = (L1 + L2 ) / (S1 + S2).

6 = 220 / ( 250/18 + S2).
(taking the right side denominator to left).

6( 250/18 + S2) = 220.
(multiplying 6 inside).

250/3 + 6 S2 = 220.
6 S2 = 220 - 250/3.
6 S2 = (660-250)/3
S2 = 410/18
( to convert this to KMPH - multiply by 18/5 )

S2 = 410/18 * 18/5
S2 = 82 KMPH

First train speed 50sec.

Second train speed?
S = l1 + l2/t1 + t2.
Relative speed = x + 50s.
X + 50s = 108+112/6+t2.
X + 50s =792/6.
6x + 300=792.
6x = 792-300.
6x = 492.
X = 492/6.
X = 82.

The answer 82 is in m/s. We want to convert it into km/hr, because in first step we convert speed into m/s by multiplying 5/18.