A boat goes downstream at a speed of 18 km/hr and upstream at a speed of \'m\' km/hr. The boat travelled 90 km downstream in a river and then returned back taking altogether 12.5 hours. Then which of the following are true ?
A. m = 12
B. m = 15
C. Speed of water current is 3 km/hr
D. Speed of water current is 1.5 km/hr
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A and C only
Time downstream + time upstream = 12.5 hours:
\( \displaystyle \frac{90}{18}+\frac{90}{m}=12.5 \)
\( \displaystyle 5+\frac{90}{m}=12.5\ \Rightarrow\ \frac{90}{m}=7.5 \)
\( \displaystyle m=12 \)
If u is the speed of the boat in still water and v the speed of the current, then u + v = 18 and u − v = 12, so the current is half the difference of the two speeds:
\( \displaystyle v=\frac{18-12}{2}=3\ \text{km/hr} \)
So m = 12 and the speed of the current is 3 km/hr.
Checking the statements
(A) m = 12 — Correct. 90/18 + 90/12 = 5 + 7.5 = 12.5 hours.
(B) m = 15 — Incorrect. With m = 15 the total time is 5 + 6 = 11 hours, not 12.5.
(C) Speed of water current is 3 km/hr — Correct. (18 − 12)/2 = 3 km/hr.
(D) Speed of water current is 1.5 km/hr — Incorrect. The current is (18 − 12)/2 = 3 km/hr.