Question : A boat covers 12 km upstream and 18 km downstream in 3 hours, while it covers 36 km upstream and 24 km downstream in $6\frac{1}{2}$ hours. What is the speed of the current?
Option 1: 1.5 km/hr
Option 2: 1 km/hr
Option 3: 2 km/hr
Option 4: 2.5 km/hr
Correct Answer: 2 km/hr
Solution :
Let the downstream speed of the boat = $u$ km/hr and the upstream speed of the boat be $v$ km/hr, then the Speed of current = $\frac{u-v}{2}$
According to the question,
$\frac{18}{u} +\frac{12}{v}=3 $ (equation 1)
$\frac{24}{u} +\frac{36}{v}=\frac{13}{2} $ (equation 2)
Multiply by 3 in equation 1, we get,
$\frac{54}{u} +\frac{36}{v}=9 $ (equation 3)
Subtract equation 2 from equation 3, we get,
$\frac{30}{u}=\frac{5}{2}$
⇒ $u$ = 12 km/hr
Substitute the value of $u$ in equation 1, we get,
$\frac{18}{12} +\frac{12}{v}=3$
⇒ $\frac{12}{v}=3-\frac{3}{2}$
⇒ $\frac{12}{v}=\frac{3}{2}$
⇒ $v$ = 8 km/hr
The speed of current is given as $\frac{12-8}{2}$ = 2 km/hr
Hence, the correct answer is 2 km/hr.
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