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06 Mar 2025, 01:41
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66% (02:57) correct
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A train after travelling 150 km meets with an accident and then proceeds at 3/5 of its former speed and arrives at its destination 8 hours late. Had the accident occurred 360 km further, it would have reached the destination 4 hours late. What is the total distance travelled by the train ?
A. 1000
B. 980
C. 840
D. 870
E. 800
A. 1000
B. 980
C. 840
D. 870
E. 800
06 Mar 2025, 01:57
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Let the distance covered after 150 km be d1
Given the distance covered after 150km is same, the train would have originally taken be t1 with speed s
After the accident, it took t1+8 with a speed of 3s/5
st1 = 3s/5 * (t1+8)
5t1 = 3t1+24
t1 = 12
Let the distance covered after 150+360 km be d2
Given the distance covered is same, the train would have originally taken be t2 with speed s
After the accident, it took t2+4 with a speed of 3s/5
st2 = 3s/5 * (t2+4)
5t1 = 3t1+12
t2 = 6
The train covered a distance of d2+360 in 12hours and d2 in 6hours
So, it covered 360km in 6hours, s = 60km/h
Total distance = 150+ d1
= 150+ s*t1
= 150 + 60*12
= 870
Given the distance covered after 150km is same, the train would have originally taken be t1 with speed s
After the accident, it took t1+8 with a speed of 3s/5
st1 = 3s/5 * (t1+8)
5t1 = 3t1+24
t1 = 12
Let the distance covered after 150+360 km be d2
Given the distance covered is same, the train would have originally taken be t2 with speed s
After the accident, it took t2+4 with a speed of 3s/5
st2 = 3s/5 * (t2+4)
5t1 = 3t1+12
t2 = 6
The train covered a distance of d2+360 in 12hours and d2 in 6hours
So, it covered 360km in 6hours, s = 60km/h
Total distance = 150+ d1
= 150+ s*t1
= 150 + 60*12
= 870
Bunuel
A train after travelling 150 km meets with an accident and then proceeds at 3/5 of its former speed and arrives at its destination 8 hours late. Had the accident occurred 360 km further, it would have reached the destination 4 hours late. What is the total distance travelled by the train ?
A. 1000
B. 980
C. 840
D. 870
E. 800
A. 1000
B. 980
C. 840
D. 870
E. 800
06 Mar 2025, 04:11
Kudos
Bookmarks
here we can see that it will take the train 4 hours less if the accident had happened 360 km further
which means 360/s +4 = 360/(3s/5)
considering speed of train was S and after accident the speed reduces to 3s/5
solving this we will get s=60kmph which is speed pf train
now using s=60 we can find reduced speed =(3/5)*60 = 36 kmph
finally for total distance D
we know d/60 = 150/60 + (d-150)/36 -8 (we are equating time, here the equation before = sign is time that it would take train if it traveled at normal speed of 60kmph without interruption)
solving this we will get total distance D=870
which means 360/s +4 = 360/(3s/5)
considering speed of train was S and after accident the speed reduces to 3s/5
solving this we will get s=60kmph which is speed pf train
now using s=60 we can find reduced speed =(3/5)*60 = 36 kmph
finally for total distance D
we know d/60 = 150/60 + (d-150)/36 -8 (we are equating time, here the equation before = sign is time that it would take train if it traveled at normal speed of 60kmph without interruption)
solving this we will get total distance D=870
