Boat and Stream / āύāĻžāĻ“ āφ⧰⧁ āϏ⧋āρāϤ


āϗ⧁⧰⧁āĻ¤ā§āĻŦāĻĒā§‚ā§°ā§āĻŖ āϏ⧂āĻ¤ā§ā§° (Boats & Streams) // Important Formulas (Boats & Streams)


1. āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— = āύāĻžāϓ⧰ āĻŦ⧇āĻ— + āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ— (Downstream Speed Boat Speed + Stream Speed)


2. āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āĻŦ⧇āĻ— = āύāĻžāϓ⧰ āĻŦ⧇āĻ— − āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ— (Upstream Speed = Boat Speed Stream Speed)


3. āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ āύāĻžāϓ⧰ āĻŦ⧇āĻ— = (āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— + āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āĻŦ⧇āĻ—) ÷ 2 [Boat Speed in Still Water = (Downstream Speed + Upstream Speed) ÷ 2]


4. āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ— = (āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— − āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āĻŦ⧇āĻ—) ÷ 2 [Stream Speed = (Downstream Speed Upstream Speed) ÷ 2]


5. āϏāĻŽāϝāĻŧ = āĻĻā§‚ā§°āĻ¤ā§āĻŦ ÷ āĻŦ⧇āĻ— (Time = Distance ÷ Speed)


6. āĻĻā§‚ā§°āĻ¤ā§āĻŦ = āĻŦ⧇āĻ— × āϏāĻŽāϝāĻŧ (Distance = Speed × Time)


7. āĻŦ⧇āĻ— = āĻĻā§‚ā§°āĻ¤ā§āĻŦ ÷ āϏāĻŽāϝāĻŧ (Speed = Distance ÷ Time)


Note: āĻāχ āϏ⧂āĻ¤ā§ā§°āϏāĻŽā§‚āĻš Panchayat Recruitment, ADRE, Assam Police, Grade-III, Grade-IV, Clerical, Banking, SSC, Railway, Group-C, Group-D āφ⧰⧁ āĻ…āĻ¨ā§āϝāĻžāĻ¨ā§āϝ āĻĒā§ā§°āϤāĻŋāϝ⧋āĻ—āĻŋāϤāĻžāĻŽā§‚āϞāĻ• āĻĒā§°ā§€āĻ•ā§āώāĻžā§° āĻŦāĻžāĻŦ⧇ āĻ…āϤāĻŋ āϗ⧁⧰⧁āĻ¤ā§āĻŦāĻĒā§‚ā§°ā§āĻŖāĨ¤ (These formulas are very important for Panchayat Recruitment, ADRE, Assam Police, Grade-III, Grade-IV, Clerical, Banking, SSC, Railway, Group-C, Group-D, and other competitive examinations.)


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1. A boat takes 2 hours to travel 30 km downstream and 3 hours to travel the same distance upstream. What is the speed of the boat in still water ? āĻĒā§ā§°āĻļā§āύ: āĻāĻ–āύ āύāĻžāĻ“āϝāĻŧ⧇ 30 āĻ•āĻŋāĻŽāĻŋ āĻ…āύ⧁āϕ⧂āϞ āϏ⧋āρāϤ⧇ (Downstream) āϝāĻžāĻŦāϞ⧈ 2 āϘāĻŖā§āϟāĻž āφ⧰⧁ āĻāϕ⧇ āĻĻā§‚ā§°āĻ¤ā§āĻŦ āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āϏ⧋āρāϤ⧇ (Upstream) āϝāĻžāĻŦāϞ⧈ 3 āϘāĻŖā§āϟāĻž āϏāĻŽāϝāĻŧ āϞāϝāĻŧāĨ¤ āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ āύāĻžāĻ“āĻ–āύ⧰ āĻŦ⧇āĻ— āĻ•āĻŋāĻŽāĻžāύ ?


Options: (A) 10 km/h | (B) 12.5 km/h | (C) 15 km/h | (D) 18 km/h


Explanation / āĻŦā§āϝāĻžāĻ–ā§āϝāĻž:


Downstream Speed / āĻ…āύ⧁āϕ⧂āϞ āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ— = 30/2 = 15 km/h


Upstream Speed / āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ— = 30/3 = 10 km/h 


Speed of Boat in Still Water / āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ āύāĻžāϓ⧰ āĻŦ⧇āĻ—


= Downstream Speed + Upstream Speed / 2 


= 15+10/2


Ans = 12.5 km/h


Trick:


Boat Speed (Still Water - āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀⧰ āĻŦ⧇āĻ—)


= Downstream Speed + Upstream Speed / 2 


Ans = 12.5 km/h


Where: D = Downstream Speed / āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— , U = Upstream Speed / āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āĻŦ⧇āĻ—


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2.The speed of a boat in still water is 18 km/h and the speed of the stream is 3 km/h. How much time will it take to travel 42 km upstream  (āĻĒā§ā§°āĻļā§āύ: āĻāĻ–āύ āύāĻžāϓ⧰ āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ āĻŦ⧇āĻ— 18 āĻ•āĻŋāĻŽāĻŋ/āϘāĻŖā§āϟāĻž āφ⧰⧁ āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ— 3 āĻ•āĻŋāĻŽāĻŋ/āϘāĻŖā§āϟāĻžāĨ¤ 42 āĻ•āĻŋāĻŽāĻŋ āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ⧇ (Upstream) āϝāĻžāĻŦāϞ⧈ āĻ•āĻŋāĻŽāĻžāύ āϏāĻŽāϝāĻŧ āϞāĻžāĻ—āĻŋāĻŦ?)


Options: (A) 2 hours / āϘāĻŖā§āϟāĻž  (B) 2.5 hours / āϘāĻŖā§āϟāĻž  (C) 3 hours / āϘāĻŖā§āϟāĻž  (D) 3.5 hours / āϘāĻŖā§āϟāĻž


Ans / āωāĻ¤ā§āϤ⧰: (C) 3 hours / āϘāĻŖā§āϟāĻž


Explanation / āĻŦā§āϝāĻžāĻ–ā§āϝāĻž:


1st: Find Upstream Speed (āĻĒā§ā§°āĻĨāĻŽā§‡ āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āĻŦ⧇āĻ— āωāϞāĻŋāϝāĻŧāĻžāĻ“)


Upstream Speed = Boat Speed − Stream Speed = 18−3 = 15 km/h


2nd: Find Time (āϏāĻŽāϝāĻŧ āωāϞāĻŋāϝāĻŧāĻžāĻ“)


Time = Distance / Speed = 42/15 = 2.8 hours ≈3 hours


Ans = 3 hours


Trick:


Upstream Speed = Boat Speed − Stream Speed


18 − 3 = 15


Then,


42 ÷ 15 = 2.8


Nearest option = 3 hours


Ans = 3 hours


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3. A boat travels 36 km downstream in 2 hours and 24 km upstream in 2 hours. What is the speed of the boat in still water ? (āĻĒā§ā§°āĻļā§āύ: āĻāĻ–āύ āύāĻžāĻ“āϝāĻŧ⧇ 36 āĻ•āĻŋāĻŽāĻŋ āĻ…āύ⧁āϕ⧂āϞ āϏ⧋āρāϤ⧇ 2 āϘāĻŖā§āϟāĻžāϤ āφ⧰⧁ 24 āĻ•āĻŋāĻŽāĻŋ āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āϏ⧋āρāϤ⧇ 2 āϘāĻŖā§āϟāĻžāϤ āĻ…āϤāĻŋāĻ•ā§ā§°āĻŽ āϕ⧰⧇āĨ¤ āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ āύāĻžāĻ“āĻ–āύ⧰ āĻŦ⧇āĻ— āĻ•āĻŋāĻŽāĻžāύ ?)


Options: (A) 12 km/h | (B) 15 km/h | (C) 18 km/h | (D) 20 km/h


Ans / āωāĻ¤ā§āϤ⧰: (B) 15 km/h


Explanation / āĻŦā§āϝāĻžāĻ–ā§āϝāĻž:


Downstream Speed / āĻ…āύ⧁āϕ⧂āϞ āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ— =36/2 = 18 km/h


Upstream Speed / āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ— = 24/2 = 12 km/h


Boat Speed in Still Water / āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ āύāĻžāϓ⧰ āĻŦ⧇āĻ— = Downstream Speed + Upstream Speed / 2 = 18 + 12 / 2 =  =15 km/h


Ans = 15 km/h


Trick: Boat Speed = (Downstream Speed + Upstream Speed) ÷ 2


= 18 + 12 / 2 = 


Ans = 15 km/h


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5. A boat moves at 16 km/h in still water. The speed of the stream is 4 km/h. How much time will it take to travel 60 km downstream ?(āĻāĻ–āύ āύāĻžāĻ“ āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ 16 āĻ•āĻŋāĻŽāĻŋ/āϘāĻŖā§āϟāĻž āĻŦ⧇āϗ⧇ āϚāϞ⧇āĨ¤ āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ— 4 āĻ•āĻŋāĻŽāĻŋ/āϘāĻŖā§āϟāĻžāĨ¤ 60 āĻ•āĻŋāĻŽāĻŋ āĻ…āύ⧁āϕ⧂āϞ⧇ (Downstream) āϝāĻžāĻŦāϞ⧈ āĻ•āĻŋāĻŽāĻžāύ āϏāĻŽāϝāĻŧ āϞāĻžāĻ—āĻŋāĻŦ ?)


Options: (A) 2 hours / āϘāĻŖā§āϟāĻž  (B) 2.5 hours / āϘāĻŖā§āϟāĻž  (C) 3 hours / āϘāĻŖā§āϟāĻž  (D) 4 hours / āϘāĻŖā§āϟāĻž


Ans / āωāĻ¤ā§āϤ⧰: (C) 3 hours / āϘāĻŖā§āϟāĻž






Explanation / āĻŦā§āϝāĻžāĻ–ā§āϝāĻž:


1st: Find Downstream Speed (āĻĒā§ā§°āĻĨāĻŽā§‡ āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— āωāϞāĻŋāϝāĻŧāĻžāĻ“āĻ•)


Downstream Speed = Boat Speed + Stream Speed = 16 + 4 = 20 km/h


2nd: Find Time (āϏāĻŽāϝāĻŧ āωāϞāĻŋāϝāĻŧāĻžāĻ“)


Time = Distance / Speed = 60 / 20 = 


Ans = 3 hours


Trick: Downstream Speed = Boat Speed + Stream Speed

16  + 4 = 20 Then,


60 ÷ 20 = 3


Ans = 3 hours


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6. The ratio of the speed of a boat in still water to the speed of the stream is 5 : 1. If the downstream speed is 24 km/h, what is the speed of the boat in still water ? (āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ āύāĻžāϓ⧰ āĻŦ⧇āĻ— āφ⧰⧁ āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ—ā§° āĻ…āύ⧁āĻĒāĻžāϤ 5 : 1āĨ¤ āϝāĻĻāĻŋ āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— (Downstream Speed) 24 āĻ•āĻŋāĻŽāĻŋ/āϘāĻŖā§āϟāĻž āĻšāϝāĻŧ, āϤ⧇āĻ¨ā§āϤ⧇ āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ āύāĻžāϓ⧰ āĻŦ⧇āĻ— āĻ•āĻŋāĻŽāĻžāύ ?)


Options: (A) 18 km/h | (B) 20 km/h | (C) 22 km/h | (D) 25 km/h


Ans / āωāĻ¤ā§āϤ⧰: (B) 20 km/h


Explanation / āĻŦā§āϝāĻžāĻ–ā§āϝāĻž:


Given / āĻĻāĻŋāϝāĻŧāĻž āφāϛ⧇:


Boat Speed : Stream Speed = 5 : 1


Let,


Boat Speed = 5x , Stream Speed = x


Downstream Speed = 5x + x =


Given,




Therefore,




Trick:


Downstream = Boat Speed + Stream Speed (āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— = āύāĻžāϓ⧰ āĻŦ⧇āĻ— + āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ—)


If ratio is 5 : 1, then downstream ratio = 6 parts.


Divide the downstream speed by 6 to get 1 part, then multiply by 5.


Ans / āωāĻ¤ā§āϤ⧰: (B) 20 km/h


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6. A boat travels 40 km downstream in the same time in which it travels 30 km upstream. What is the ratio of downstream speed to upstream speed ? (āĻāĻ–āύ āύāĻžāĻ“āϝāĻŧ⧇ āϝāĻŋ āϏāĻŽāϝāĻŧāϤ 40 āĻ•āĻŋāĻŽāĻŋ āĻ…āύ⧁āϕ⧂āϞ⧇ (Downstream) āϝāĻžāϝāĻŧ, āĻāϕ⧇ āϏāĻŽāϝāĻŧāϤ 30 āĻ•āĻŋāĻŽāĻŋ āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ⧇ (Upstream) āϝāĻžāϝāĻŧāĨ¤ āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— āφ⧰⧁ āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āĻŦ⧇āĻ—ā§° āĻ…āύ⧁āĻĒāĻžāϤ āĻ•āĻŋāĻŽāĻžāύ ?)


Options: (A) 3 : 4  (B) 4 : 3  (C) 5 : 4  (D) 6 : 5


Ans / āωāĻ¤ā§āϤ⧰: (B) 4 : 3


Explanation / āĻŦā§āϝāĻžāĻ–ā§āϝāĻž:


Given / āĻĻāĻŋāϝāĻŧāĻž āφāϛ⧇:



  • Downstream Distance = 40 km

  • Upstream Distance = 30 km

  • Time is same / āϏāĻŽāϝāĻŧ āϏāĻŽāĻžāύ


We know : Speed = Distance / Time


When time is the same, Speed Ratio = Distance Ratio


Therefore,


                Downstream Speed : Upstream Speed = 40 : 30


Ans = 4 : 3


Trick:


Same Time ⇒ Speed ∝ Distance (āĻāϕ⧇ āϏāĻŽāϝāĻŧ ⇒ āĻŦ⧇āĻ— ∝ āĻĻā§‚ā§°āĻ¤ā§āĻŦ)


Time same → Compare only distances. (āϏāĻŽāϝāĻŧ āϏāĻŽāĻžāύ → āĻ•ā§‡ā§ąāϞ āĻĻā§‚ā§°āĻ¤ā§āĻŦā§° āĻ…āύ⧁āĻĒāĻžāϤ āϞāĻ“āĻ•āĨ¤)


40 : 30 = 4 : 3


Ans / āωāĻ¤ā§āϤ⧰: (B) 4 : 3


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7. The downstream speed is 18 km/h and the upstream speed is 8 km/h. What is the speed of the boat in still water ? (āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— 18 āĻ•āĻŋāĻŽāĻŋ/āϘāĻŖā§āϟāĻž āφ⧰⧁ āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āĻŦ⧇āĻ— 8 āĻ•āĻŋāĻŽāĻŋ/āϘāĻŖā§āϟāĻžāĨ¤ āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ āύāĻžāĻ“āĻ–āύ⧰ āĻŦ⧇āĻ— āĻ•āĻŋāĻŽāĻžāύ ?)


Options: (A) 11 km/h | (B) 12 km/h | (C) 13 km/h | (D) 14 km/h


Ans / āωāĻ¤ā§āϤ⧰: (C) 13 km/h


Explanation / āĻŦā§āϝāĻžāĻ–ā§āϝāĻž:


We know / āφāĻŽāĻŋ āϜāĻžāύ⧋:


Boat Speed in Still Water = Downstream Speed + Upstream Speed / 2 = 18+8 / 2 = 26/2 =


Ans = 13 km/h


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8. A boat travels 72 km downstream in 4 hours. If the speed of the stream is 4 km/h, what is the speed of the boat in still water ? (āĻāĻ–āύ āύāĻžāĻ“āϝāĻŧ⧇ 72 āĻ•āĻŋāĻŽāĻŋ āĻ…āύ⧁āϕ⧂āϞ⧇ (Downstream) 4 āϘāĻŖā§āϟāĻžāϤ āĻ…āϤāĻŋāĻ•ā§ā§°āĻŽ āϕ⧰⧇āĨ¤ āϝāĻĻāĻŋ āϏ⧋āρāϤ⧰ āĻŦ⧇āĻ— 4 āĻ•āĻŋāĻŽāĻŋ/āϘāĻŖā§āϟāĻž āĻšāϝāĻŧ, āϤ⧇āĻ¨ā§āϤ⧇ āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāύ⧀āϤ āύāĻžāĻ“āĻ–āύ⧰ āĻŦ⧇āĻ— āĻ•āĻŋāĻŽāĻžāύ ?)


Options / āĻŦāĻŋāĻ•āĻ˛ā§āĻĒāϏāĻŽā§‚āĻš: (A) 12 km/h | (B) 14 km/h | (C) 16 km/h | (D) 18 km/h


Ans / āωāĻ¤ā§āϤ⧰: (B) 14 km/h


Explanation / āĻŦā§āϝāĻžāĻ–ā§āϝāĻž:

1st: Find Downstream Speed (āĻĒā§ā§°āĻĨāĻŽā§‡ āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— āωāϞāĻŋāϝāĻŧāĻžāĻ“)


Downstream Speed = Distance / Time = = 18 km/h


2nd: Find Boat Speed (āύāĻžāϓ⧰ āĻŦ⧇āĻ— āωāϞāĻŋāϝāĻŧāĻžāĻ“āĻ•)


Boat Speed = Downstream Speed − Stream Speed =18 − 4 =


Ans = 14 km


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9. A boat takes a total of 6 hours to travel 15 km upstream and 21 km downstream. If the downstream speed is 7 km/h, what is the upstream speed ? (āĻāĻ–āύ āύāĻžāĻ“āϝāĻŧ⧇ 15 āĻ•āĻŋāĻŽāĻŋ āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ⧇ āφ⧰⧁ 21 āĻ•āĻŋāĻŽāĻŋ āĻ…āύ⧁āϕ⧂āϞ⧇ āϝāĻžāĻŦāϞ⧈ āĻŽā§āĻ  6 āϘāĻŖā§āϟāĻž āϏāĻŽāϝāĻŧ āϞāϝāĻŧāĨ¤ āϝāĻĻāĻŋ āĻ…āύ⧁āϕ⧂āϞ āĻŦ⧇āĻ— 7 āĻ•āĻŋāĻŽāĻŋ/āϘāĻŖā§āϟāĻž āĻšāϝāĻŧ, āϤ⧇āĻ¨ā§āϤ⧇ āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āĻŦ⧇āĻ— āĻ•āĻŋāĻŽāĻžāύ ?)

Options / āĻŦāĻŋāĻ•āĻ˛ā§āĻĒāϏāĻŽā§‚āĻš:(A) 4 km/h | (B) 5 km/h | (C) 6 km/h | (D) 8 km/h

 

 Ans / āωāĻ¤ā§āϤ⧰: (B) 5 km/h


Explanation / āĻŦā§āϝāĻžāĻ–ā§āϝāĻž:


Time taken downstream (āĻ…āύ⧁āϕ⧂āϞ⧇ āĻ¯ā§‹ā§ąāĻžā§° āϏāĻŽāϝāĻŧ)


Time = Distance / Speed = 21/7 =


Time taken upstream (āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ⧇ āĻ¯ā§‹ā§ąāĻžā§° āϏāĻŽāϝāĻŧ) : Total time = 6 hours


Upstream Time = 6 3 = 3 hours


Upstream Speed (āĻĒā§ā§°āϤāĻŋāϕ⧂āϞ āĻŦ⧇āĻ—)


= 15/3 = 



Trick:


Find downstream time: 21 ÷ 7 = 3


Remaining time:


Upstream speed:


Ans = 5 km/h


Note


Speed = Distance ÷ Time (āĻŦ⧇āĻ— = āĻĻā§‚ā§°āĻ¤ā§āĻŦ ÷ āϏāĻŽāϝāĻŧ)


First find the known journey's time (āφāĻ—āϤ⧇ āϜāύāĻž āϝāĻžāĻ¤ā§ā§°āĻžā§° āϏāĻŽāϝāĻŧ āωāϞāĻŋāϝāĻŧāĻžāĻ“), then subtract from total time.(āϤāĻžā§° āĻĒāĻŋāĻ›āϤ āĻŽā§āĻ  āϏāĻŽāϝāĻŧā§° āĻĒā§°āĻž āĻŦāĻŋāϝāĻŧā§‹āĻ—)


Ans / āωāĻ¤ā§āϤ⧰: (B) 5 km/h