Boat P takes 1.8 hour more than boat Q to cover 54 km downstream. To cover
the same distance in equal time, boat P has to increase its speed by 25%. What
can be the possible speed of boat P, if the speed of stream is 1 km/hr?
नावp 54 किमी धारा अनुग्णवाह की और को तय करने के लिए नाव से 1.8 घंटे अधिक लेती
है। समान समय में समान दरी को तय करने के लिए नाव P को अपनी गति 25% तक बढ़ानी
होगी। नाव P की संभावित गाति कितनी हो सकती है. यदि धारा की गति 1 किमी/घंटा है।
A) 2 km/hr
B) 4 km/hr
C) S km/hr
D) 0.5 km/hr
E) 6 km/hr
Answers
Given : Boat P takes 1.8 hour more than boat Q to cover 54 km downstream. To cover the same distance in equal time, boat P has to increase its speed by 25%. What can be the possible speed of boat P, the speed of stream is 1 km/hr
To Find : possible speed of boat P
A) 2 km/hr
B) 4 km/hr
C) S km/hr
D) 0.5 km/hr
E) 6 km/hr
Solution:
Speed of Boat P = 4P km/hr
speed of stream is 1 km/hr
Down stream speed = 4P + 1 km/hr
Time taken to cover 54 km = 54/ (4P + 1) hr
boat P has to increase its speed by 25%
=> 4P + (25/100)4P = 5P
Down stream speed = 5P + 1 km/hr
Time taken to cover 54 km = 54/ (5P + 1) hr
54/ (4P + 1) = 54/ (5P + 1) + 1.8
=> 54(5P + 1) = 54(4P + 1) + 1.8 (5P + 1)(4P+1)
=> 30(5P + 1) = 30(4P+1) + (5P + 1)(4P+1)
=> (5P + 1)(4P+1) - 30P = 0
=> 20P² + 9P + 1 - 30P = 0
=> 20P² - 21P + 1 = 0
=> 20P² - 20P - P + 1 = 0
=> 20P(P - 1) - 1(P - 1) = 0
=> (20 P - 1) (P - 1) = 0
=> P = 1/20 , P = 1
=> 4P = 4/20 =0.2 or 4P = 4
There is no meaning of boat speed being less than stream speed hence 4P = 0.2 neglected
Hence Speed of Boat P = 4 km/hr
Learn More:
A boat goes 2km upstream and 3km down stream in 20min it goes ...
brainly.in/question/6491842
a motorboat whose speed is 18 km per hour in still water takes 1 ...
brainly.in/question/7322647