Question : Dharmendra can row 80 km upstream and 110 km downstream in 13 hours. Also, he can row 60 km upstream and 88 km downstream in 10 hours. What is the speed (in km/hr ) of the current?
Option 1: 6
Option 2: 16
Option 3: 10
Option 4: 12
Correct Answer: 6
Solution :
Let downstream speed and upstream speeds be $u$ km/hr and $v$ km/hr, respectively.
Dharmendra can row 80 km upstream and 110 km downstream in 13 hours
$\frac{110}{u}+\frac{80}{v}=13$..................(I)
He can row 60 km upstream and 88 km downstream in 10 hours.
$\frac{88}{u}+\frac{60}{v}=10$..................(II)
Equation (I) is multiplied by 3 and equation (II) is multiplied by 4.
We get,
$\frac{330}{u}+\frac{240}{v}=39$..................(III)
$\frac{352}{u}+\frac{240}{v}=40$..................(IV)
Subtracting equation (III) from equation (IV), we get,
$\frac{22}{u}=1$
⇒ $u=22$ km/hr
Putting $u = 22$ in equation (I), we get,
$\frac{110}{22}+\frac{80}{v}=13$
⇒$\frac{80}{v}=8$
⇒$v=10$ km/hr
Speed of the current = $\frac{1}{2}$ × (Downstream speed – Upstream speed)
= $\frac{1}{2}$ (22 – 10) = 6 km/hr
Hence, the correct answer is 6.
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