In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for both quantities and chose the correct option.
Quantity A: A man takes 11/9 times downstream time to row upstream keeping the distance same in both cases. What is the speed of boat (m/s) in still water if it takes 6 hours to travel 80 km in downstream?
Quantity B: A boat running in upstream covers 20 km distance in 3 hours while covering the same distance in downstream it takes 2 hours. What is the speed of the boat in still water (m/s)?Solving for Quantity A -
Distance cover = 80 km
Time taken = 6 hours
Speed of downstream = 80/6 = 13.33 kmph
Speed of downstream = Speed of boat + speed of stream ---- (I)
Speed of upstream = speed of boat - speed of stream ---- (II)
Let assume Speed of boat as x kmph ,
Speed of stream as y kmph,
Time taken in upstream is 11/9 times more,
Time taken in upstream = (11/9) × 6 = 7.33 hours
Speed of upstream = 80/7.33 = 10.91 kmph
Substitute the values in Eq (I) and Eq (II);
⇒ x + y = 13.33
⇒ x - y = 10.91
By eliminating y terms in above equation,
⇒ 2x = 24.24
⇒ x = 12.12 kmph
Convert the vale in m/s by multiplying it 18/5,
Speed of boat = 12.12 × (5/18) = 3.36 m/s
Solving for Quantity B -
Let assume speed of boat in still water = x kmph
Speed of stream = y kmph
For the speed of boat in upstream,
Distance covered = 20 km
Time taken = 3 hour
Speed of boat in upstream = 20/3 = 6.67 kmph
For the speed of boat in downstream,
Distance covered = 20 km
Time taken = 2 hour
Speed of boat in downstream = 20/2 = 10 kmph
Speed of downstream = Speed of boat + speed of stream = x + y = 10
Speed of upstream = speed of boat - speed of stream = x - y = 6.67
By eliminating y terms,
⇒ 2x = 16.67
⇒ x = 8.335 kmph
Convert the value in m/s by multiplying 5/18,
⇒ x = 8.335 × (5/18) = 2.315 m/s
∴ Quantity A > Quantity B