Correct Answer - Option 2 :
\(21\frac{2}{3}\;sec\)
Given:
Distance travelled by boat = 130 metre
Speed of stream = 6 m/s
Concept used:
If the speed of boat in still water is ‘x’ km/hr and speed of stream is ‘y’ km/hr, then:
Upstream speed = Speed of boat - Speed of stream = (x – y)
Downstream speed = Speed of boat + Speed of stream = (x + y)
Calculations:
Let the speed of boats be 5x and 3x
∴ For faster boat
Downstream speed = Speed of boat + Speed of stream = 5x + 6
⇒ 5x + 6 = (130/5) = 26
⇒ 5x = 20
⇒ x = 4
∴ Speed of Faster boat = 5 × 4 = 20 km/hr
Speed of slower boat = 3 × 4 = 12 km/hr
∴ Time taken by the slower boat to cover 130 m upstream
⇒ Time = Distance/Speed
⇒ Time = 130/(12 – 6)
⇒ Time = 65/3
∴ Time taken by the slower boat = 65/3 \( = 21\frac{2}{3}\)