CBSE Class 10 Math Question Paper 2018 | Q23A

Question 23A: A motor boat whose speed is 18 km/hr in still water takes 1hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Video Explanation

Explanatory Answer | CBSE Class 10 Math Paper 2018 Q23A

Still water speed of motor boat = 18 km/hr
Let the speed of stream = s km/hr

Upstream speed of boat = (18 - s) km/hr
Downstream speed of boat = (18 + s) km/hr

Time taken to travel 24 km upstream = \\frac{24}{18 - S})
Time taken to travel 24 km downstream = \\frac{24}{18 + S})

Time for upstream = Time for downstream + 1 hour
\\frac{24}{18 - s}) = \\frac{24}{18 + s}) + 1
\\frac{24(18 + s) − 24(18 − s)}{(18 − s) (18 + s)}) = 1
2 × 24 × s = 18² - s²
Or s² + 48s - 324 = 0
s² + 54s – 6s - 324 = 0
s = -54 or s = 6

Speed has to be positive.
∴ Speed of stream = 6 km/hr