Correct Answer - Option 1 : 9 km/h and 2 km/h
Given:
Time taken to cover 44 km downstream and 42 km upstream = 10 hours
Time taken to cover 38.5 km downstream and 63 km upstream = 12.5 Hours
Formula Used:
Time = Distance/Speed
Downstream Speed (D) = Speed of Boat (x) + Speed of Stream (y)
Upstream Speed (U) = Speed of Boat (x) - Speed of Stream (y)
Speed of Boat = (D + U)/2
Speed of Stream = (D - U)/2
Calculation:
Let the downstream speed be D and upstream speed be U
(44/D) + (42/U) = 10 ____(i)
(38.5/D) + (63/U) = 12.5 ____(ii)
Multiply equation i by 3 and equation ii by 2
(132/D) + (126/U) = 30 ____(i)
(77/D) + (126/U) = 25 ____(ii)
Subtract equation ii from equation i
[(132/D) + (126/U) = 30] – [(77/D) + (126/U) = 25]
⇒ (55/D) = 5
⇒ D = (55/5)
⇒ D = 11 km/h
Putting value of D in equation i
(44/11) + (42/U) = 10
⇒ 4 + (42/U) = 10
⇒ (42/U) = 6
⇒ U = 42/6 = 7 km/h
Speed of Boat = (11 + 7)/2
⇒ Speed of Boat = 9 km/h
Speed of Stream = (11 – 7)/2
⇒ Speed of Stream = 2 Km/h
∴ The speed of boat and stream is 9 km/h and 2 km/h respectively.