Question

Upstream speed of a motorboat is 70% of that downstream speed. The motorboat goes 220 km downstream but while returning the same distance in upstream, the rate of stream was double of itself. In this way, the motorboat takes the total time of 31 hours. What was the difference between time taken to go 220 km downstream and return the same distance in upstream?

• A. 7 hours
• B. 8 hours
• C. 11 hours
• D. 9 hours

Answer 1

The Correct Option is D

The correct option is (D): 9 hours.
Let the speed of motorboat in still water = u km per hour
Rate of stream = v km per hour
Upstream speed = u - v km per hour
Downstream speed = u + v km per hour
According to the question, 70% of (u + v) = (u - v)
\(\frac{(u - v)}{(u + v)}\) = \(\frac{7}{10}\)
\(\frac{u}{v}\) = \(\frac{17}{3}\)
Let u be 17a then, v = 3a
According to the question, 220/20a + 220/(17a - 6a) = 31 hours
\(\frac{11}{a}\)+ \(\frac{20}{a}\) =\(\frac{31}{a}\) = 31 hours
a = 1
Therefore, the time taken to go 220 km downstream = \(\frac{220}{20}\) =11 hours
The time taken to return 220 km upstream = \(\frac{220}{11}\) = 20 hours
The required difference = 20-11=9 hours.