A boat can cover 36 km down stream and 16 km up stream in 10 hours. It can cover 3 km down stream and 1.2 km up stream in 48 minutes. What is the speed (in km/hr of the boat when going up stream?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 4.
let the speed of the boat = x
speed of the stream = y
ATQ -
⇒ (36)/(x + y) + (16)/(x - y) = 10
⇒ (36x - 36y + 16x + 16y)/((x - y)(x + y)) = 10
⇒ 52x - 20y =10(x - y)(x + y) ...(1
Also, 3/(x + y) + 1.2/(x - y) = 4/5
⇒ (3x - 3y + 1.2x + 1.2y)/((x - y)(x + y)) = 4/5
⇒ 4.2x - 1.8y = (4/5)(x + y)(x - y) ....(2
Dividing eq(1 and (2 we get -
⇒ 104x - 40y =105x - 45y
⇒ -x = -5y
⇒ x = 5y
Substituting in the above equation -
3/(5y + y) + 1.2/(5y - y) =4/5
⇒ (1/2y) + (3/10y) = 4/5
8/10y = 4/5
y = 1 km/hr
x = 5 km/hr
Upstream speed = x - y = 5 - 1= 4 km/hr