Boat and Stream / āĻ¨āĻžāĻ āĻā§°ā§ āĻ¸ā§āĻāĻ¤ 1
āĻā§ā§°ā§āĻ¤ā§āĻŦāĻĒā§ā§°ā§āĻŖ āĻ¸ā§āĻ¤ā§ā§° (Boats & Streams) // Important Formulas (Boats & Streams)
1. āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ + āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ (Downstream Speed = Boat Speed + Stream Speed)
2. āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ − āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ (Upstream Speed = Boat Speed − Stream Speed)
3. āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻ¨āĻžāĻā§° āĻŦā§āĻ = (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ + āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ) ÷ 2 [Boat Speed in Still Water = (Downstream Speed + Upstream Speed) ÷ 2]
4. āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ = (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ − āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ) ÷ 2 [Stream Speed = (Downstream Speed − Upstream Speed) ÷ 2]
5. āĻ¸āĻŽāĻ¯āĻŧ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻŦā§āĻ (Time = Distance ÷ Speed)
6. āĻĻā§ā§°āĻ¤ā§āĻŦ = āĻŦā§āĻ × āĻ¸āĻŽāĻ¯āĻŧ (Distance = Speed × Time)
7. āĻŦā§āĻ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻ¸āĻŽāĻ¯āĻŧ (Speed = Distance ÷ Time)
Note: āĻāĻ āĻ¸ā§āĻ¤ā§ā§°āĻ¸āĻŽā§āĻš Panchayat Recruitment, ADRE, Assam Police, Grade-III, Grade-IV, Clerical, Banking, SSC, Railway, Group-C, Group-D āĻā§°ā§ āĻ
āĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯ āĻĒā§ā§°āĻ¤āĻŋāĻ¯ā§āĻāĻŋāĻ¤āĻžāĻŽā§āĻ˛āĻ āĻĒā§°ā§āĻā§āĻˇāĻžā§° āĻŦāĻžāĻŦā§ āĻ
āĻ¤āĻŋ āĻā§ā§°ā§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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Q1. āĻāĻāĻ¨ āĻ¨āĻžāĻā§° āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻŦā§āĻ 10 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻā§°ā§ āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ 2 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻžāĨ¤ āĻ¨āĻžāĻāĻāĻ¨ 48 āĻāĻŋāĻŽāĻŋ āĻ
āĻ¨ā§āĻā§āĻ˛ā§ āĻā§°ā§ 48 āĻāĻŋāĻŽāĻŋ āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ā§ āĻ¯āĻžāĻ¯āĻŧāĨ¤ āĻŽā§āĻ āĻāĻŋāĻŽāĻžāĻ¨ āĻ¸āĻŽāĻ¯āĻŧ āĻ˛āĻžāĻāĻŋāĻŦ ? A boat has a speed of 10 km/h in still water, and the speed of the stream is 2 km/h. How much total time will it take to travel 48 km downstream and 48 km upstream ?
A) 4 hours (ā§Ē āĻāĻŖā§āĻāĻž) B) 9 hours (ā§¯ āĻāĻŖā§āĻāĻž) C) 10 hours (ā§§ā§Ļ āĻāĻŖā§āĻāĻž) D) 12 hours (ā§§ā§¨ āĻāĻŖā§āĻāĻž)
Ans / āĻāĻ¤ā§āĻ¤ā§°: C) 10 hours (ā§§ā§Ļ āĻāĻŖā§āĻāĻž)
Explanation / āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž:
- Downstream speed = 10 + 2 = 12 km/h (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ = 10 + 2 = 12 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Upstream speed = 10 − 2 = 8 km/h (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ = 10 − 2 = 8 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Time downstream = 48 ÷ 12 = 4 hours (āĻ
āĻ¨ā§āĻā§āĻ˛ā§ āĻ¸āĻŽāĻ¯āĻŧ = 48 ÷ 12 = 4 āĻāĻŖā§āĻāĻž)
- Time upstream = 48 ÷ 8 = 6 hours (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ā§ āĻ¸āĻŽāĻ¯āĻŧ = 48 ÷ 8 = 6 āĻāĻŖā§āĻāĻž)
- Total time = 4 + 6 = 10 hours (āĻŽā§āĻ āĻ¸āĻŽāĻ¯āĻŧ = 4 + 6 = 10 āĻāĻŖā§āĻāĻž )
Trick:
- Downstream (āĻ
āĻ¨ā§āĻā§āĻ˛) Speed = Boat Speed + Stream Speed (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ + āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ)
- Upstream (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛) Speed = Boat Speed − Stream Speed (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ − āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ)
- Time = Distance ÷ Speed (āĻ¸āĻŽāĻ¯āĻŧ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻŦā§āĻ)
Calculation / āĻšāĻŋāĻāĻžāĻĒ:
- Downstream (āĻ
āĻ¨ā§āĻā§āĻ˛): 48 ÷ 12 = 4 hours (4 āĻāĻŖā§āĻāĻž)
- Upstream (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛): 48 ÷ 8 = 6 hours (6 āĻāĻŖā§āĻāĻž)
- Total Time (āĻŽā§āĻ āĻ¸āĻŽāĻ¯āĻŧ): 4 + 6 = 10 hours (10 āĻāĻŖā§āĻāĻž)
Q2. āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ 25 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻā§°ā§ āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ 15 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻžāĨ¤ āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻ¨āĻžāĻā§° āĻŦā§āĻ āĻā§°ā§ āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻā§° āĻ
āĻ¨ā§āĻĒāĻžāĻ¤ āĻāĻŋāĻŽāĻžāĻ¨ ? The downstream speed of a boat is 25 km/h and the upstream speed is 15 km/h. What is the ratio of the speed of the boat in still water to the speed of the stream ?
A) 4 : 1 B) 5 : 1 C) 6 : 1 D) 3 : 1
Ans / āĻāĻ¤ā§āĻ¤ā§°: A) 4 : 1
Explanation / āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž
- Boat speed in still water = (25 + 15) ÷ 2 = 20 km/h (āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻ¨āĻžāĻā§° āĻŦā§āĻ = (25 + 15) ÷ 2 = 20 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Stream speed = (25 − 15) ÷ 2 = 5 km/h (āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ = (25 − 15) ÷ 2 = 5 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Ratio (āĻ
āĻ¨ā§āĻĒāĻžāĻ¤) = 20 : 5 = 4 : 1
Trick / āĻā§āĻļāĻ˛
- Boat Speed = (Downstream + Upstream) ÷ 2 [āĻ¨āĻžāĻā§° āĻŦā§āĻ = (āĻ
āĻ¨ā§āĻā§āĻ˛ + āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛) ÷ 2]
- Stream Speed = (Downstream − Upstream) ÷ 2 [āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ = (āĻ
āĻ¨ā§āĻā§āĻ˛ − āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛) ÷ 2]
- Ratio = Boat Speed : Stream Speed (āĻ
āĻ¨ā§āĻĒāĻžāĻ¤ = āĻ¨āĻžāĻā§° āĻŦā§āĻ : āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ )
Q3. āĻāĻāĻ¨ āĻ¨āĻžāĻ 56 āĻāĻŋāĻŽāĻŋ āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ā§ 7 āĻāĻŖā§āĻāĻžāĻ¤ āĻ
āĻ¤āĻŋāĻā§ā§°āĻŽ āĻā§°ā§āĨ¤ āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ 2 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻš'āĻ˛ā§ āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻ¨āĻžāĻā§° āĻŦā§āĻ āĻāĻŋāĻŽāĻžāĻ¨ ? A boat travels 56 km upstream in 7 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water ?
A) 8 km/h B) 9 km/h C) 10 km/h D) 12 km/h
Ans / āĻāĻ¤ā§āĻ¤ā§°: C) 10 km/h
Explanation / āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž
- Upstream speed = 56 ÷ 7 = 8 km/h (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = 56 ÷ 7 = 8 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Boat speed = Upstream speed + Stream speed (āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻ¨āĻžāĻā§° āĻŦā§āĻ = āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ + āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ)
- 8 + 2 = 10 km/h (āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
Trick / āĻā§āĻļāĻ˛
- Upstream Speed = Distance ÷ Time (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻ¸āĻŽāĻ¯āĻŧ)
- Boat Speed = Upstream Speed + Stream Speed (āĻ¨āĻžāĻā§° āĻŦā§āĻ = āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ + āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ)
Q4. āĻāĻāĻ¨ āĻ¨āĻžāĻ 90 āĻāĻŋāĻŽāĻŋ āĻ
āĻ¨ā§āĻā§āĻ˛ā§ 5 āĻāĻŖā§āĻāĻžāĻ¤ āĻā§°ā§ 60 āĻāĻŋāĻŽāĻŋ āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ā§ 5 āĻāĻŖā§āĻāĻžāĻ¤ āĻ¯āĻžāĻ¯āĻŧāĨ¤ āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ āĻāĻŋāĻŽāĻžāĻ¨ ? A boat travels 90 km downstream in 5 hours and 60 km upstream in 5 hours. What is the speed of the stream ?
A) 2 km/h B) 3 km/h C) 4 km/h D) 5 km/h
Ans / āĻāĻ¤ā§āĻ¤ā§°: B) 3 km/h
Explanation / āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž
- Downstream speed = 90 ÷ 5 = 18 km/h (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = 90 ÷ 5 = 18 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Upstream speed = 60 ÷ 5 = 12 km/h (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = 60 ÷ 5 = 12 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Stream speed = (18 − 12) ÷ 2 = 3 km/h (āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ = (18 − 12) ÷ 2 = 3 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
Trick / āĻā§āĻļāĻ˛
- Downstream Speed = Distance ÷ Time (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻ¸āĻŽāĻ¯āĻŧ)
- Upstream Speed = Distance ÷ Time (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻ¸āĻŽāĻ¯āĻŧ)
- Stream Speed = (Downstream − Upstream) ÷ 2 (āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ = (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ − āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ) ÷ 2)
Q5. āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻā§° āĻĻā§āĻŦāĻŋāĻā§āĻŖāĨ¤ āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ 4 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻš'āĻ˛ā§ āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻ¨āĻžāĻā§° āĻŦā§āĻ āĻāĻŋāĻŽāĻžāĻ¨ ? The downstream speed is twice the upstream speed. If the speed of the stream is 4 km/h, what is the speed of the boat in still water ?
A) 8 km/h B) 10 km/h C) 12 km/h D) 16 km/h
Ans / āĻāĻ¤ā§āĻ¤ā§°: C) 12 km/h
Explanation / āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž
- Let Upstream speed = x (āĻ§ā§°āĻž, āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = x)
- Downstream speed = 2x (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = 2x)
- Stream speed = (Downstream − Upstream) ÷ 2 [āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ = (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ − āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ) ÷ 2]
- 4 = (2x − x) ÷ 2
- x = 8 km/h (āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Boat speed (āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻ¨āĻžāĻā§° āĻŦā§āĻ) = (16 + 8) ÷ 2 = 12 km/h (āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
Trick / āĻā§āĻļāĻ˛
- Boat Speed = (Downstream + Upstream) ÷ 2 [āĻ¨āĻžāĻā§° āĻŦā§āĻ = (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ + āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ) ÷ 2]
- Stream Speed = (Downstream − Upstream) ÷ 2 [āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ = (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ − āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ) ÷ 2]
Q6. āĻāĻāĻ¨ āĻ¨āĻžāĻ 24 āĻāĻŋāĻŽāĻŋ āĻ
āĻ¨ā§āĻā§āĻ˛ā§ āĻā§°ā§ 16 āĻāĻŋāĻŽāĻŋ āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ā§ āĻ¯āĻžāĻŦāĻ˛ā§ āĻ¸āĻŽāĻžāĻ¨ āĻ¸āĻŽāĻ¯āĻŧ āĻ˛āĻ¯āĻŧāĨ¤ āĻ
āĻ¨ā§āĻā§āĻ˛ āĻā§°ā§ āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻā§° āĻ
āĻ¨ā§āĻĒāĻžāĻ¤ āĻāĻŋāĻŽāĻžāĻ¨ ? A boat takes the same time to travel 24 km downstream and 16 km upstream. What is the ratio of the downstream speed to the upstream speed ?
A) 2 : 3 B) 3 : 2 C) 4 : 3 D) 5 : 4
Ans / āĻāĻ¤ā§āĻ¤ā§°: B) 3 : 2
Explanation / āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž
- Time = Distance ÷ Speed (āĻ¸āĻŽāĻ¯āĻŧ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻŦā§āĻ)
- Since the time is the same, (āĻ¯āĻŋāĻšā§āĻ¤ā§ āĻ¸āĻŽāĻ¯āĻŧ āĻ¸āĻŽāĻžāĻ¨,)
24 / Downstream Speed(āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ) = 16 / Upstream Speed(āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ)â
Therefore, Downstream Speed : Upstream Speed(āĻ¸ā§āĻ¯āĻŧā§, āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ : āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ) = 24 : 16 = 3 : 2â
Trick / āĻā§āĻļāĻ˛
- If time is the same, Speed ∝ Distance (āĻ¯āĻĻāĻŋ āĻ¸āĻŽāĻ¯āĻŧ āĻ¸āĻŽāĻžāĻ¨ āĻšāĻ¯āĻŧ, āĻ¤ā§āĻ¨ā§āĻ¤ā§ āĻŦā§āĻ ∝ āĻĻā§ā§°āĻ¤ā§āĻŦ)
- Speed Ratio = Distance Ratio (āĻŦā§āĻā§° āĻ
āĻ¨ā§āĻĒāĻžāĻ¤ = āĻĻā§ā§°āĻ¤ā§āĻŦā§° āĻ
āĻ¨ā§āĻĒāĻžāĻ¤)
- 24 : 16 = 3 : 2
Q7. āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻāĻāĻ¨ āĻ¨āĻžāĻā§° āĻŦā§āĻ 22 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻā§°ā§ āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ 3 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻžāĨ¤ 75 āĻāĻŋāĻŽāĻŋ āĻ
āĻ¨ā§āĻā§āĻ˛ā§ āĻ¯āĻžāĻŦāĻ˛ā§ āĻāĻŋāĻŽāĻžāĻ¨ āĻ¸āĻŽāĻ¯āĻŧ āĻ˛āĻžāĻāĻŋāĻŦ ? The speed of a boat in still water is 22 km/h and the speed of the stream is 3 km/h. How much time will it take to travel 75 km downstream ?
A) 2 hours B) 3 hours C) 4 hours D) 5 hours
Ans / āĻāĻ¤ā§āĻ¤ā§°: B) 3 hours (3 āĻāĻŖā§āĻāĻž)
Explanation / āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž
- Downstream Speed = Boat Speed + Stream Speed (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ + āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ) = 22 + 3 = 25 km/h (25 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Time = Distance ÷ Speed (āĻ¸āĻŽāĻ¯āĻŧ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻŦā§āĻ) = 75 ÷ 25 = 3 hours (3 āĻāĻŖā§āĻāĻž)
Trick / āĻā§āĻļāĻ˛
- Downstream Speed = Boat Speed + Stream Speed (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ + āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ)
- Time = Distance ÷ Speed (āĻ¸āĻŽāĻ¯āĻŧ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻŦā§āĻ)
- 75 ÷ (22 + 3) = 75 ÷ 25 = 3 hours (3 āĻāĻŖā§āĻāĻž)
Q8. āĻāĻāĻ¨ āĻ¨āĻžāĻ 84 āĻāĻŋāĻŽāĻŋ āĻ
āĻ¨ā§āĻā§āĻ˛ā§ 6 āĻāĻŖā§āĻāĻžāĻ¤ āĻ¯āĻžāĻ¯āĻŧāĨ¤ āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ 3 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻš'āĻ˛ā§ āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ āĻāĻŋāĻŽāĻžāĻ¨ āĻš'āĻŦ ? A boat travels 84 km downstream in 6 hours. If the speed of the stream is 3 km/h, what is the upstream speed of the boat ?
A) 8 km/h B) 10 km/h C) 11 km/h D) 12 km/h
Ans / āĻāĻ¤ā§āĻ¤ā§°: A) 8 km/h
Explanation / āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž
- Downstream Speed = Distance ÷ Time (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻ¸āĻŽāĻ¯āĻŧ) = 84 ÷ 6 = 14 km/h (14 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Boat Speed = Downstream Speed − Stream Speed (āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻ¨āĻžāĻā§° āĻŦā§āĻ = āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ − āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ) = 14 − 3 = 11 km/h (11 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Upstream Speed = Boat Speed − Stream Speed (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ − āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ) = 11 − 3 = 8 km/h (8 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
Trick / āĻā§āĻļāĻ˛
- Downstream Speed = Distance ÷ Time (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻ¸āĻŽāĻ¯āĻŧ)
- Boat Speed = Downstream Speed − Stream Speed (āĻ¨āĻžāĻā§° āĻŦā§āĻ = āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ − āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ)
- Upstream Speed = Boat Speed − Stream Speed (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ − āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ)
- 84 ÷ 6 = 14 → 14 − 3 = 11 → 11 − 3 = 8 km/h (8 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
Q9. āĻāĻāĻ¨ āĻ¨āĻžāĻā§° āĻ¸ā§āĻĨāĻŋā§° āĻĒāĻžāĻ¨ā§āĻ¤ āĻŦā§āĻ 15 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻā§°ā§ āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ 5 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻžāĨ¤ 40 āĻāĻŋāĻŽāĻŋ āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ā§ āĻā§°ā§ 40 āĻāĻŋāĻŽāĻŋ āĻ
āĻ¨ā§āĻā§āĻ˛ā§ āĻ¯āĻžāĻŦāĻ˛ā§ āĻŽā§āĻ āĻāĻŋāĻŽāĻžāĻ¨ āĻ¸āĻŽāĻ¯āĻŧ āĻ˛āĻžāĻāĻŋāĻŦ ? A boat has a speed of 15 km/h in still water and the speed of the stream is 5 km/h. How much total time will it take to travel 40 km upstream and 40 km downstream ?
A) 5 hours B) 6 hours C) 7 hours D) 4 hours
Ans / āĻāĻ¤ā§āĻ¤ā§°: B) 6 hours (6 āĻāĻŖā§āĻāĻž)
Explanation / āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž
- Downstream Speed = Boat Speed + Stream Speed (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ + āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ) = 15 + 5 = 20 km/h (20 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Upstream Speed = Boat Speed − Stream Speed (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ − āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ) = 15 − 5 = 10 km/h (10 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)
- Downstream Time = Distance ÷ Speed (āĻ
āĻ¨ā§āĻā§āĻ˛ā§ āĻ¸āĻŽāĻ¯āĻŧ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻŦā§āĻ) = 40 ÷ 20 = 2 hours (2 āĻāĻŖā§āĻāĻž)
- Upstream Time = Distance ÷ Speed (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ā§ āĻ¸āĻŽāĻ¯āĻŧ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻŦā§āĻ) = 40 ÷ 10 = 4 hours (4 āĻāĻŖā§āĻāĻž)
- Total Time = 2 + 4 = 6 hours (6 āĻāĻŖā§āĻāĻž)
Trick / āĻā§āĻļāĻ˛
- Downstream Speed = Boat Speed + Stream Speed (āĻ
āĻ¨ā§āĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ + āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ)
- Upstream Speed = Boat Speed − Stream Speed (āĻĒā§ā§°āĻ¤āĻŋāĻā§āĻ˛ āĻŦā§āĻ = āĻ¨āĻžāĻā§° āĻŦā§āĻ − āĻ¸ā§āĻāĻ¤ā§° āĻŦā§āĻ)
- Time = Distance ÷ Speed (āĻ¸āĻŽāĻ¯āĻŧ = āĻĻā§ā§°āĻ¤ā§āĻŦ ÷ āĻŦā§āĻ)
- 40 ÷ 20 + 40 ÷ 10 = 2 + 4 = 6 hours (6 āĻāĻŖā§āĻāĻž)