Question 28 (Choice 1) - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at May 29, 2023 by Teachoo

A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours lessthan the scheduled time. And, if the train were slower by 6 km/hr ; it would have taken 6 hours more than the scheduled time. Find the length of the journey.

Question 28 (Choice 1) A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/hr ; it would have taken 6 hours more than the scheduled time. Find the length of the journey.
Let Speed of train = x km/h
& Time taken = y hours.
We know that,
Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒
Distance = Speed × Time
Distance = xy
If the train would have been 6 km/h faster I.e.
Speed = x + 6
It would have taken 4 hours less i.e.
Time = y − 4
Now,
Distance = Speed × time
Distance = (x + 6) (y − 4)
Putting Distance = xy from Equation (1)
xy = (x + 6) (y − 4)
xy = x (y − 4) + 6 (y − 4)
xy = xy − 4x + 6y − 24
4x − 6y + 24 = xy − xy
4x − 6y + 24 = 0
2(2x − 3y + 12) = 0
2x − 3y + 12 = 0
Also,
If the train were slower by 6km/h
Speed = x − 6,
it would have taken 6 hours more
Time = y + 6.
Now
Distance = Speed × time
Distance = (x − 6) (y + 6)
Putting Distance = xy from equation (1)
xy = (x − 6) (y + 6)
xy = x (y + 6) − 6(y + 6)
xy = xy + 6x − 6y − 36
xy − xy = 6x − 6y − 36
6x − 6y − 36 = 0
6(x − y − 6) = 0
x − y − 6 = 0
Hence, the equations are
2x − 3y + 12 = 0 …(2)
x − y − 6 = 0 …(3)
From equation (3)
x − y − 6 = 0
x = y + 6
Putting (4) in equation (2)
2x − 3y + 12 = 0
2(y + 6) − 3y + 12 = 0
2y + 12 − 3y + 12 = 0
2y − 3y + 12 + 12 = 0
−y + 24 = 0
24 = y
y = 24
Putting y = 12 in equation (4)
x = y + 6
x = 24 + 6
x = 30
Thus,
Speed of train = x = 30 km/ h
& Time taken by the train = y = 24 hours
Now,
Distance = Speed × time
Distance = 30 × 24
Distance = 720 km

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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