A motor boat goes from A to B and comes back located at bank of river. If speed of motor boat becomes double in still water, it takes 20 % of its original time to travel from A to B and B to A. Find speed of motorboat is how many times of flow of river?
Answer & explanation
Correct answer: option 3
Let boat's speed = A
River flow's speed = B
Speed of boat in downstream = A + B
Speed of boat in upstream = A - B
Distance = \(\frac{Product\;of\;speed}{sum\;of\;speed}\) × Time
ATQ,
⇒ \(\frac{(A+B) (A-B)}{(A+B)+(A-B)}\) × T = \(\frac{(2A+B) (2A-B)}{(2A+B)+(2A-B)}\) × 20% of T
⇒ \(\frac{A^2 - B^2}{2A}\) × 5T = \(\frac{4A^2 - B^2}{4B}\) × T
⇒ 10 A2 - 10B2 = 4A2 - B2
⇒ 6A2 = 9B2
⇒ A = \(\sqrt {\frac{3}{2}}\) × B