A boat goes 27 km upstream and 33 km downstream in 6 hours . In the same time it can go 36 km upstream and 22 km downstream . How much time will it take to go 36 km upstream and 44 km downstream?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 8 h.
Given :
27km upstream and 33km downstream = 6 hours
36km upstream and 22km downstream = 6 hours
Formula used :
If the speed of boat = x
speed of stream = y
Speed of upstream = (x - y) km/h ----- (1)
Speed of downstream = (x + y) km/h ----- (2)
Calculations :
Using equation (1) and (2)
⇒ 33/(x + y) + 27/(x - y) = 6 ---- (3)
⇒ 22/(x + y) + 36/(x - y) = 6 ---- (4)
Equating equations (3) and (4)
⇒ 33/(x + y) + 27/(x - y) = 22/(x + y) + 36/(x - y)
⇒ 11/(x + y) = 9/(x - y)
⇒ 2x = 20y
⇒ x = 10y
Put the value of x in equation (3)
⇒ 3/y + 3/y = 6
⇒ y = 1
⇒ x = 10
Speed of downstream = x + y = 11
Speed of upstream = x - y = 9
Time taken to go 36 km upstream and 44 km downstream
⇒ 36/9 + 44/11
⇒ 4 + 4 = 8 hours