Boat and Stream / āύāĻžāĻ āĻā§°ā§ āϏā§āĻāϤ
āĻā§ā§°ā§āϤā§āĻŦāĻĒā§ā§°ā§āĻŖ āϏā§āϤā§ā§° (Boats & Streams) // Important Formulas (Boats & Streams)
1. āĻ
āύā§āĻā§āϞ āĻŦā§āĻ = āύāĻžāĻā§° āĻŦā§āĻ + āϏā§āĻāϤ⧰ āĻŦā§āĻ (Downstream Speed = Boat Speed + Stream Speed)
2. āĻĒā§ā§°āϤāĻŋāĻā§āϞ āĻŦā§āĻ = āύāĻžāĻā§° āĻŦā§āĻ − āϏā§āĻāϤ⧰ āĻŦā§āĻ (Upstream Speed = Boat Speed − Stream Speed)
3. āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ āύāĻžāĻā§° āĻŦā§āĻ = (āĻ
āύā§āĻā§āϞ āĻŦā§āĻ + āĻĒā§ā§°āϤāĻŋāĻā§āϞ āĻŦā§āĻ) ÷ 2 [Boat Speed in Still Water = (Downstream Speed + Upstream Speed) ÷ 2]
4. āϏā§āĻāϤ⧰ āĻŦā§āĻ = (āĻ
āύā§āĻā§āϞ āĻŦā§āĻ − āĻĒā§ā§°āϤāĻŋāĻā§āϞ āĻŦā§āĻ) ÷ 2 [Stream Speed = (Downstream Speed − Upstream Speed) ÷ 2]
5. āϏāĻŽāϝāĻŧ = āĻĻā§ā§°āϤā§āĻŦ ÷ āĻŦā§āĻ (Time = Distance ÷ Speed)
6. āĻĻā§ā§°āϤā§āĻŦ = āĻŦā§āĻ × āϏāĻŽāϝāĻŧ (Distance = Speed × Time)
7. āĻŦā§āĻ = āĻĻā§ā§°āϤā§āĻŦ ÷ āϏāĻŽāϝāĻŧ (Speed = Distance ÷ Time)
Note: āĻāĻ āϏā§āϤā§ā§°āϏāĻŽā§āĻš Panchayat Recruitment, ADRE, Assam Police, Grade-III, Grade-IV, Clerical, Banking, SSC, Railway, Group-C, Group-D āĻā§°ā§ āĻ
āύā§āϝāĻžāύā§āϝ āĻĒā§ā§°āϤāĻŋāϝā§āĻāĻŋāϤāĻžāĻŽā§āϞāĻ āĻĒā§°ā§āĻā§āώāĻžā§° āĻŦāĻžāĻŦā§ āĻ
āϤāĻŋ āĻā§ā§°ā§āϤā§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.)
==================================================================
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: āĻāĻāύ āύāĻžāĻāϝāĻŧā§ 30 āĻāĻŋāĻŽāĻŋ āĻ
āύā§āĻā§āϞ āϏā§āĻāϤ⧠(Downstream) āϝāĻžāĻŦāϞ⧠2 āĻāĻŖā§āĻāĻž āĻā§°ā§ āĻāĻā§ āĻĻā§ā§°āϤā§āĻŦ āĻĒā§ā§°āϤāĻŋāĻā§āϞ āϏā§āĻāϤ⧠(Upstream) āϝāĻžāĻŦāϞ⧠3 āĻāĻŖā§āĻāĻž āϏāĻŽāϝāĻŧ āϞāϝāĻŧāĨ¤ āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ āύāĻžāĻāĻāύ⧰ āĻŦā§āĻ āĻāĻŋāĻŽāĻžāύ ?
Options: (A) 10 km/h | (B) 12.5 km/h | (C) 15 km/h | (D) 18 km/h
Explanation / āĻŦā§āϝāĻžāĻā§āϝāĻž:
Downstream Speed / āĻ
āύā§āĻā§āϞ āϏā§āĻāϤ⧰ āĻŦā§āĻ = 30/2 = 15 km/h
Upstream Speed / āĻĒā§ā§°āϤāĻŋāĻā§āϞ āϏā§āĻāϤ⧰ āĻŦā§āĻ = 30/3 = 10 km/h
Speed of Boat in Still Water / āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ āύāĻžāĻā§° āĻŦā§āĻ
= Downstream Speed + Upstream Speed / 2
â = 15+10/2 = 12.5 km/h
Ans = 12.5 km/h
Trick:
Boat Speed (Still Water - āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§ā§° āĻŦā§āĻ)
= Downstream Speed + Upstream Speed / 2 = 15+10â / 2 = 12.5
Ans = 12.5 km/h
Where: D = Downstream Speed / āĻ
āύā§āĻā§āϞ āĻŦā§āĻ , U = Upstream Speed / āĻĒā§ā§°āϤāĻŋāĻā§āϞ āĻŦā§āĻ
===============================================================
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: āĻāĻāύ āύāĻžāĻā§° āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ āĻŦā§āĻ 18 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻā§°ā§ āϏā§āĻāϤ⧰ āĻŦā§āĻ 3 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻžāĨ¤ 42 āĻāĻŋāĻŽāĻŋ āĻĒā§ā§°āϤāĻŋāĻā§āϞ⧠(Upstream) āϝāĻžāĻŦāϞ⧠āĻāĻŋāĻŽāĻžāύ āϏāĻŽāϝāĻŧ āϞāĻžāĻāĻŋāĻŦ?)
Options: (A) 2 hours / āĻāĻŖā§āĻāĻž (B) 2.5 hours / āĻāĻŖā§āĻāĻž (C) 3 hours / āĻāĻŖā§āĻāĻž (D) 3.5 hours / āĻāĻŖā§āĻāĻž
Ans / āĻāϤā§āϤ⧰: (C) 3 hours / āĻāĻŖā§āĻāĻž
Explanation / āĻŦā§āϝāĻžāĻā§āϝāĻž:
1st: Find Upstream Speed (āĻĒā§ā§°āĻĨāĻŽā§ āĻĒā§ā§°āϤāĻŋāĻā§āϞ āĻŦā§āĻ āĻāϞāĻŋāϝāĻŧāĻžāĻ)
Upstream Speed = Boat Speed − Stream Speed = 18−3 = 15 km/h
2nd: Find Time (āϏāĻŽāϝāĻŧ āĻāϞāĻŋāϝāĻŧāĻžāĻ)
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
===============================================================
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: āĻāĻāύ āύāĻžāĻāϝāĻŧā§ 36 āĻāĻŋāĻŽāĻŋ āĻ
āύā§āĻā§āϞ āϏā§āĻāϤ⧠2 āĻāĻŖā§āĻāĻžāϤ āĻā§°ā§ 24 āĻāĻŋāĻŽāĻŋ āĻĒā§ā§°āϤāĻŋāĻā§āϞ āϏā§āĻāϤ⧠2 āĻāĻŖā§āĻāĻžāϤ āĻ
āϤāĻŋāĻā§ā§°āĻŽ āĻā§°ā§āĨ¤ āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ āύāĻžāĻāĻāύ⧰ āĻŦā§āĻ āĻāĻŋāĻŽāĻžāύ ?)
Options: (A) 12 km/h | (B) 15 km/h | (C) 18 km/h | (D) 20 km/h
Ans / āĻāϤā§āϤ⧰: (B) 15 km/h
Explanation / āĻŦā§āϝāĻžāĻā§āϝāĻž:
Downstream Speed / āĻ
āύā§āĻā§āϞ āϏā§āĻāϤ⧰ āĻŦā§āĻ =36/2 = 18 km/h
Upstream Speed / āĻĒā§ā§°āϤāĻŋāĻā§āϞ āϏā§āĻāϤ⧰ āĻŦā§āĻ = 24/2 = 12 km/h
Boat Speed in Still Water / āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ āύāĻžāĻā§° āĻŦā§āĻ = Downstream Speed + Upstream Speed / 2 = 18 + 12 / 2 = 30/2â =15 km/h
Ans = 15 km/h
Trick: Boat Speed = (Downstream Speed + Upstream Speed) ÷ 2
= 18 + 12 / 2 = 15
Ans = 15 km/h
===============================================================
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 ?(āĻāĻāύ āύāĻžāĻ āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ 16 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻŦā§āĻā§ āĻāϞā§āĨ¤ āϏā§āĻāϤ⧰ āĻŦā§āĻ 4 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻžāĨ¤ 60 āĻāĻŋāĻŽāĻŋ āĻ
āύā§āĻā§āϞ⧠(Downstream) āϝāĻžāĻŦāϞ⧠āĻāĻŋāĻŽāĻžāύ āϏāĻŽāϝāĻŧ āϞāĻžāĻāĻŋāĻŦ ?)
Options: (A) 2 hours / āĻāĻŖā§āĻāĻž (B) 2.5 hours / āĻāĻŖā§āĻāĻž (C) 3 hours / āĻāĻŖā§āĻāĻž (D) 4 hours / āĻāĻŖā§āĻāĻž
Ans / āĻāϤā§āϤ⧰: (C) 3 hours / āĻāĻŖā§āĻāĻž
Explanation / āĻŦā§āϝāĻžāĻā§āϝāĻž:
1st: Find Downstream Speed (āĻĒā§ā§°āĻĨāĻŽā§ āĻ
āύā§āĻā§āϞ āĻŦā§āĻ āĻāϞāĻŋāϝāĻŧāĻžāĻāĻ)
Downstream Speed = Boat Speed + Stream Speed = 16 + 4 = 20 km/h
2nd: Find Time (āϏāĻŽāϝāĻŧ āĻāϞāĻŋāϝāĻŧāĻžāĻ)
Time = Distance / Speed = 60 / 20 = 3 hours
Ans = 3 hours
Trick: Downstream Speed = Boat Speed + Stream Speed
16 + 4 = 20 Then,
60 ÷ 20 = 3
Ans = 3 hours
================================================================
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 ? (āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ āύāĻžāĻā§° āĻŦā§āĻ āĻā§°ā§ āϏā§āĻāϤ⧰ āĻŦā§āĻā§° āĻ
āύā§āĻĒāĻžāϤ 5 : 1āĨ¤ āϝāĻĻāĻŋ āĻ
āύā§āĻā§āϞ āĻŦā§āĻ (Downstream Speed) 24 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻšāϝāĻŧ, āϤā§āύā§āϤ⧠āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ āύāĻžāĻā§° āĻŦā§āĻ āĻāĻŋāĻŽāĻžāύ ?)
Options: (A) 18 km/h | (B) 20 km/h | (C) 22 km/h | (D) 25 km/h
Ans / āĻāϤā§āϤ⧰: (B) 20 km/h
Explanation / āĻŦā§āϝāĻžāĻā§āϝāĻž:
Given / āĻĻāĻŋāϝāĻŧāĻž āĻāĻā§:
Boat Speed : Stream Speed = 5 : 1
Let,
Boat Speed = 5x , Stream Speed = x
Downstream Speed = 5x + x = 6x
Given,
6x = 24
x = 4
Therefore,
Boat Speed = 5x = 5 × 4 = 20 km/h
Ans = 20 km/h
Trick:
Downstream = Boat Speed + Stream Speed (āĻ
āύā§āĻā§āϞ āĻŦā§āĻ = āύāĻžāĻā§° āĻŦā§āĻ + āϏā§āĻāϤ⧰ āĻŦā§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 / āĻāϤā§āϤ⧰: (B) 20 km/h
================================================================
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 ? (āĻāĻāύ āύāĻžāĻāϝāĻŧā§ āϝāĻŋ āϏāĻŽāϝāĻŧāϤ 40 āĻāĻŋāĻŽāĻŋ āĻ
āύā§āĻā§āϞ⧠(Downstream) āϝāĻžāϝāĻŧ, āĻāĻā§ āϏāĻŽāϝāĻŧāϤ 30 āĻāĻŋāĻŽāĻŋ āĻĒā§ā§°āϤāĻŋāĻā§āϞ⧠(Upstream) āϝāĻžāϝāĻŧāĨ¤ āĻ
āύā§āĻā§āϞ āĻŦā§āĻ āĻā§°ā§ āĻĒā§ā§°āϤāĻŋāĻā§āϞ āĻŦā§āĻā§° āĻ
āύā§āĻĒāĻžāϤ āĻāĻŋāĻŽāĻžāύ ?)
Options: (A) 3 : 4 (B) 4 : 3 (C) 5 : 4 (D) 6 : 5
Ans / āĻāϤā§āϤ⧰: (B) 4 : 3
Explanation / āĻŦā§āϝāĻžāĻā§āϝāĻž:
Given / āĻĻāĻŋāϝāĻŧāĻž āĻāĻā§:
- Downstream Distance = 40 km
- Upstream Distance = 30 km
- Time is same / āϏāĻŽāϝāĻŧ āϏāĻŽāĻžāύ
We know : Speed = Distance / Timeâ
When time is the same, Speed Ratio = Distance Ratio
Therefore,
Downstream Speed : Upstream Speed = 40 : 30 = 4 : 3
Ans = 4 : 3
Trick:
Same Time ⇒ Speed ∝ Distance (āĻāĻā§ āϏāĻŽāϝāĻŧ ⇒ āĻŦā§āĻ ∝ āĻĻā§ā§°āϤā§āĻŦ)
Time same → Compare only distances. (āϏāĻŽāϝāĻŧ āϏāĻŽāĻžāύ → āĻā§ā§ąāϞ āĻĻā§ā§°āϤā§āĻŦā§° āĻ
āύā§āĻĒāĻžāϤ āϞāĻāĻāĨ¤)
40 : 30 = 4 : 3
Ans / āĻāϤā§āϤ⧰: (B) 4 : 3
===============================================================
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
āύā§āĻā§āϞ āĻŦā§āĻ 18 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻā§°ā§ āĻĒā§ā§°āϤāĻŋāĻā§āϞ āĻŦā§āĻ 8 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻžāĨ¤ āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ āύāĻžāĻāĻāύ⧰ āĻŦā§āĻ āĻāĻŋāĻŽāĻžāύ ?)
Options: (A) 11 km/h | (B) 12 km/h | (C) 13 km/h | (D) 14 km/h
Ans / āĻāϤā§āϤ⧰: (C) 13 km/h
Explanation / āĻŦā§āϝāĻžāĻā§āϝāĻž:
We know / āĻāĻŽāĻŋ āĻāĻžāύā§:
Boat Speed in Still Water = Downstream Speed + Upstream Speed / 2 = 18+8 / 2 = 26/2 = 13 km/h
Ans = 13 km/h
========================================================================
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 ? (āĻāĻāύ āύāĻžāĻāϝāĻŧā§ 72 āĻāĻŋāĻŽāĻŋ āĻ
āύā§āĻā§āϞ⧠(Downstream) 4 āĻāĻŖā§āĻāĻžāϤ āĻ
āϤāĻŋāĻā§ā§°āĻŽ āĻā§°ā§āĨ¤ āϝāĻĻāĻŋ āϏā§āĻāϤ⧰ āĻŦā§āĻ 4 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻšāϝāĻŧ, āϤā§āύā§āϤ⧠āϏā§āĻĨāĻŋā§° āĻĒāĻžāύā§āϤ āύāĻžāĻāĻāύ⧰ āĻŦā§āĻ āĻāĻŋāĻŽāĻžāύ ?)
Options / āĻŦāĻŋāĻāϞā§āĻĒāϏāĻŽā§āĻš: (A) 12 km/h | (B) 14 km/h | (C) 16 km/h | (D) 18 km/h
Ans / āĻāϤā§āϤ⧰: (B) 14 km/h
Explanation / āĻŦā§āϝāĻžāĻā§āϝāĻž:
1st: Find Downstream Speed (āĻĒā§ā§°āĻĨāĻŽā§ āĻ
āύā§āĻā§āϞ āĻŦā§āĻ āĻāϞāĻŋāϝāĻŧāĻžāĻ)
Downstream Speed = Distance / Time = 72/4â = 18 km/h
2nd: Find Boat Speed (āύāĻžāĻā§° āĻŦā§āĻ āĻāϞāĻŋāϝāĻŧāĻžāĻāĻ)
Boat Speed = Downstream Speed − Stream Speed =18 − 4 = 14 km/h
Ans = 14 km
===========================================================
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 ? (āĻāĻāύ āύāĻžāĻāϝāĻŧā§ 15 āĻāĻŋāĻŽāĻŋ āĻĒā§ā§°āϤāĻŋāĻā§āϞ⧠āĻā§°ā§ 21 āĻāĻŋāĻŽāĻŋ āĻ
āύā§āĻā§āϞ⧠āϝāĻžāĻŦāϞ⧠āĻŽā§āĻ 6 āĻāĻŖā§āĻāĻž āϏāĻŽāϝāĻŧ āϞāϝāĻŧāĨ¤ āϝāĻĻāĻŋ āĻ
āύā§āĻā§āϞ āĻŦā§āĻ 7 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻšāϝāĻŧ, āϤā§āύā§āϤ⧠āĻĒā§ā§°āϤāĻŋāĻā§āϞ āĻŦā§āĻ āĻāĻŋāĻŽāĻžāύ ?)
Options / āĻŦāĻŋāĻāϞā§āĻĒāϏāĻŽā§āĻš:(A) 4 km/h | (B) 5 km/h | (C) 6 km/h | (D) 8 km/h
Ans / āĻāϤā§āϤ⧰: (B) 5 km/h
Explanation / āĻŦā§āϝāĻžāĻā§āϝāĻž:
Time taken downstream (āĻ
āύā§āĻā§āϞ⧠āϝā§ā§ąāĻžā§° āϏāĻŽāϝāĻŧ)
Time = Distance / Speed = 21/7 = 3 hours
Time taken upstream (āĻĒā§ā§°āϤāĻŋāĻā§āϞ⧠āϝā§ā§ąāĻžā§° āϏāĻŽāϝāĻŧ) : Total time = 6 hours
Upstream Time = 6 − 3 = 3 hours
Upstream Speed (āĻĒā§ā§°āϤāĻŋāĻā§āϞ āĻŦā§āĻ)
Speed = Distanceâ / Time = 15/3 = 5 km/h
Ans = 5 km/h
Trick:
Find downstream time: 21 ÷ 7 = 3
Remaining time: 6 - 3 = 3
Upstream speed: 15 ÷ 3 = 5
Ans = 5 km/h
Note:
Speed = Distance ÷ Time (āĻŦā§āĻ = āĻĻā§ā§°āϤā§āĻŦ ÷ āϏāĻŽāϝāĻŧ)
First find the known journey's time (āĻāĻāϤ⧠āĻāύāĻž āϝāĻžāϤā§ā§°āĻžā§° āϏāĻŽāϝāĻŧ āĻāϞāĻŋāϝāĻŧāĻžāĻ), then subtract from total time.(āϤāĻžā§° āĻĒāĻŋāĻāϤ āĻŽā§āĻ āϏāĻŽāϝāĻŧā§° āĻĒā§°āĻž āĻŦāĻŋāϝāĻŧā§āĻ)
Ans / āĻāϤā§āϤ⧰: (B) 5 km/h