12. After going 4/5 of my journey , I find that I have covered 25 km. how much journey is
still left?
Answers
Answer:
Let the speed of the train=x km\hr
Length of the journey=y km.
Time taken=
y
x
According to the first condition.
Speed for the first 30 km = x km/hr
speed for the remaining (y−30) km =
5
4
km/hr
∴ time taken to cover 30 km =
x
30
time taken to cover (y−30)=
5
4x
y−30
=
4x
5
(y−30)
According to the problem
⇒
x
30
+
4x
5
(y−30)=
x
y
+
60
45
⇒
x
30
+
4x
5y−150
=
x
y
+
4
3
⇒120+5y−150=4y+3x
⇒y−3x=30⇔3x−y=−30 ....(1)
According to the second condition.
Speed for the first 48 km = x km/hr
speed for the remaining (y−48) km =
5
4
km/hr
∴ time taken to cover 48 km =
x
48
time taken to cover (y−48)=
4x/5
y−48
=
4x
5
(y−48)
According to the problem
⇒
x
48
+
4x
5
(y−48)=
x
y
+
60
36
⇒
x
30
+
4x
5y−150
=
x
y
+
5
3
⇒
4x
192+5y−240
=
5x
5y+3x
⇒
4x
5x−48
=
5x
5y+3x
⇒25y−240=20y+12x
⇒−12x+5y=240⇔12x−5y=−240 ........(2)
multiply eq 1 by 5
⇒15x−5y=−150 ........(3)
Substract eq2 and eq3
⇒3x=90⇒x=30
put x=30 in eq1
⇒3×30−y=−30
⇒y=120
Let the speed of the train=30 km/hr
Length of the journey=120 km.
Step-by-step explanation:
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Answer:
4/5×25/100=x
4/5×4=x
4/5×1/4=x
4/20=x
5=x