Question

a train travelledat one thirds of its usual speed ,and hence reached the destination 30 minutes after the scheduled time. on its return journey, the train initially travelled at its usual speed for 5 minutes but the stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time,is nearest to​

Answer 1

Step-by-step explanation:

Given a train travelled at one thirds of its usual speed and hence reached the destination 30 minutes after the scheduled time. on its return journey, the train initially travelled at its usual speed for 5 minutes but the stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at a scheduled time.

• Assume the scheduled speed is d and the normal time taken is t
• Now if it is travelling at d/3, then the time taken will be d + 30 min
•                                                                                          = d + ½ hrs.
• So distance travelled is same in both cases.
• So d x t = d/3 x (t + ½ )
• So 3t = t + ½  
• Or 2t = ½  
• Or t = ¼ hrs
•     t = 15 min
• So the train takes15 min to move from one place to another.
• So while returning it travels at its usual speed for 5 min.
• Assuming speed is d we have
• distance = d x 5/60 = d/12
• Also it stops for 4 min
• So total time elapsed will be 5 + 4 = 9 min
• Again total journey will be d x ¼ = d/4 kms, of which it has already travelled d/12 kms
• So remaining distance will be d/4 – d/12
•                                             = 3d – d / 12
•                                             = 2d / 12
•                                             = d/6 kms
• So initially we have 15 min, and elapsed time will be 9 min and so 6 min is left.
• So in 6 min it needs to travel d/6 kms.
• So the speed will be d/6 / 6/60
•                             = d/6 x 60 / 6
•                              = 5d/3
• The train has to travel at 5d/3 to reach its scheduled destination.at the same time.
• Now the percentage increase in its speed will be 5d/3 – d  
•                                                                               = 2d/3 / d (original speed) x 100
•                                                                               = 200 / 3
•                                                                               = 67%
• So 67% will be the increase in its speed.

Reference link will be

https://brainly.in/question/6017792