UPSC CDS 1 2022 Math Paper

Given:
Train X takes 2 hours less than a train Y
Distance between two cities 192km
Average speeds differ by 16km∕hr
Formula Used:
Speed = Distance ∕ Time
Calculation:
According to the question
X is faster train since it takes less time than y to cover a fixed distance
Let the time taken by train X be xhr
So, the time is taken by Y be (x+2)hr
Now, According to the question
⇒‌

192

x

−‌

192

x+2

=16
⇒‌

12

x

−‌

12

x+2

=1
From here, we can use the option to find directly the answer otherwise follow the given solution
⇒12(x+2)−12x=x(x+2)
⇒24=x2+2x
⇒x2+2x−24=0
⇒x2+6x−4x−24=0
⇒x(x+6)−4(x+6)=0
⇒(x+6)(x−4)=0
⇒x=−6‌ or ‌x=4
We know that time can not be negative
So, x=4
∴ The time taken by the faster train to cover the distance is 4hr :