UPSC CDS 2 2021 Math Paper

Let speed of stream be xkm∕h.
Speed of boat downstream
=(30+x)km∕h
Speed of boat upstream =(30−x)km∕h
Distance travelled downstream
=60km
Distance travelled upstream
=60km
Time taken by boat in upstream
‌‌=‌

‌ distance travelled upstream ‌

‌ Speed upstream ‌

‌‌=‌

60

(30−x)

Time taken by boat in downstream
=‌

‌ distance travelled downstream ‌

‌ Speed downstream ‌

=‌

60

30+x

Total time taken =‌

9

2

h
‌

9

2

=‌

60

30−x

+‌

60

30+x

⇒‌

9

2

=‌

60(30+x)+60(30−x)

900−x2

⇒‌

9

2

=‌

3600

900−x2

⇒‌

1

2

=‌

400

900−x2

⇒900−x2=800
⇒x2=100
⇒x=10km∕h
Hence, the speed of the stream is 10km∕h.