UPSC CDS 2 2019 Math Paper

(a) Let the speed of train be x‌km∕h and car y‌km∕h .
According to the question,
‌

120

x

+‌

480

y

=11‌‌‌⋅⋅⋅⋅⋅⋅⋅(i)
‌

200

x

+‌

400

y

=11‌

2

3

‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii)
To multiply Eq. (i) by 5 and Eq. (ii) by 3 , and subtracting, we get
‌

600

x

+‌

2400

y

−‌

600

x

−‌

1200

y

=55−35
‌

1200

y

=20
⇒‌‌y=60km∕h
On putting y=60 in Eq. (i), we get
‌

120

x

+‌

480

60

‌‌=11
⇒‌‌‌

120

x

‌‌=11−8
x‌‌=40km∕hr
∴‌‌‌ Required ratio ‌‌‌=‌

y

x

=‌

60

40

‌‌=‌

3

2

=3:2