A boat can go 40 km downstream and 25 km upstream in 7 hours and 30 minutes. It can go 48 km downstream and 36 km upstream in 10 hours. What is the speed (in km/h) of the boat in still water?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 9.
Given that:
A boat can go 40 km downstream and 25 km upstream in 7 hours and 30 minutes
It can go 48 km downstream and 36 km upstream in 10 hours
Let the speed of the boat be x km/h and the speed of the stream be y km/h;
So,
The downstream speed = x + y
The upstream speed = x - y
Formula used:
Time = Distance/Speed
According to the question
⇒ 40/(x + y) + 25/(x - y) = 7.5 .........(1
⇒ 48/(x + y) + 36/(x - y) = 10 ..........(2
5 × Equation (2) - 6 × Equation (1) :
⇒ 30/(x - y) = 50 - 45 = 5
⇒ x - y = 6 .....(3
Put this value in the equation (2
⇒ 48/(x + y) + 36/6 = 10
⇒ x + y = 12 .....(4
Adding Equation (3 and Equation (4
⇒ 2x = 6 + 12 = 18
⇒ x = 18/2 = 9 km/h
Hence, the speed of the boat in still water is 9 km/h