Question

A train travels 300 km at a uniform speed . if the speed of the train has been 5km/hr more , it would have taken 2 hours less for the same journey . find the usual speed of the train

Answer 1

ORIGINAL.....
let speed be s
let time be t
d= 300Km
speed=distance/time
s=300/t
ts=300-------------eq.1

New....
New Speed = 5+ s
New time = t-2
d=300
speed=d/t
(s+5)=300/t-2
(s+5)(t-2)=300
st-2s+5t-10=300
(ts=300)--------------eq.1
So,
300-2s+5t-10=300
5t-10=2s
(5t-10)/2-------------eq.2
placing value of eq.2 in eq.1
t×(5t-10) /2=300
5t²-10t=600
5t²-10t-600=0
5t(t-12)+50(t-12)=0
(t-12)(5t+50)=0
t-12=0. 5t + 50=0
t=12. t=-10(not possible)

So, Speed = Distance/Time
=300/12
=}25km/hr. ANS

HOPE this method is clear to u....ty

Answer 2

Answer:

Let the original speed of the train be y km / hr .

A.T.Q.

$\displaystyle{\frac{300}{y} -\frac{300}{y+5} =2 }$

300 ( y + 5 ) - 300 y = 2 y ( y + 5 )

y² + 5 y - 750 = 0

y² + 30 y - 25 y - 750 = 0

( y + 30 ( y -25 ) = 0

y = - 30 or y = 25

Since , speed of train can't be negative .

Therefore , the original speed of the train is 25 km / hr .