Shortcut Tricks to Solve Boats and Streams Questions

March 15, 2017    

INTRODUCTION:

Downstream:If the boat is moving in the direction of the stream.
Upstream: If the boat is moving in the direction opposite to the direction of the stream.
Assume the speed of the boat in still water as: ‘b’ kilometres per hour (kmph).
Take the speed of the stream as:  ‘s’ kmph.
Hence Aggregate Downstream Speed = b + s kmph. (Boat is moving with the steam of water).
Upstream Net Speed = b - s km/hr. (Boat is moving against the direction of the stream).
Speed of Boat in Still Water:   ½ (Downward Speed + Upward Speed) 
Proof of Basic Formula                
½ (Downstream Speed + Upstream Speed) = ½ [b + s + (b-s)] = ½ (2b) = b 
(Proved as per the assumption) 
Speed of Stream: ½ (Downward Speed – Upward Speed)
Proof of Basic Formula 
½ (Downward Speed – Upward Speed) = ½ [b + s – (b-s)] = ½ [b + s - b + s] = ½ (2 s} = s 
(Proved as per the assumption).

 ALWAYS REMEMBER:
  • Speed of boat is always greater than the speed of the stream. 
  • Downstream speed is always greater than the upward speed.

EXAMPLES:

Example 1. 

A man can row a boat @ 9 kmph in still water. He takes double the time to move upstream than to move the downstream – the same distance. Find the speed of the stream.

Solution:

ATQ (According to Question) and formula given above:
→Let the downward time = 1 hour and so the upward time = 2 hours.
→1/9+s = 2/9-s (Since distance is the same)
→18 + 2 s = 9 – s (By cross multiplication)
→18 – 9 = s + 2 s
→9 = 3 s
Hence s or Speed of stream = 9/3 = 3 kmph Answer.
OR
Simply
→b + s = 2(b –s)
→i.e. b + s = 2b – 2s
→i.e. s + 2s = 2b –b
Or
→b = 3s or 9 = 3s (b = 9 is given) = 3 kmph Answer

Example 2.

A boat runs at 20 kmph along the stream and 10 kmph against the stream. Find the ratio of speed of the boat in still water to that of the speed of the stream.

Solution:

→ ATQ (According to Question) and formula given above:
→ Speed of Boat = ½ (20 + 10) = 15 kmph.
→ Speed of Stream = ½ (20 – 10) = 5 kmph.
→ Ratio: 15:5 = 3:1 Answer.

Example 3.

Find the time taken by the boatman to row 4 kilometres downstream and return to his starting point, if the speed or rate of stream is 2 kilometres per hour and the speed of the boat is 6 kilometres per hour.

Solution: 

ATQ (According to Question) and formula given above:
→ Time = Distance/Speed
→ Time taken = 4/6+2 + 4/6-2 = 4/8 + 4/4 = 0.5 + 1 = 1.5 Hour.

Example 4.

If the speed of the stream is 2 km per hour, and the speed of the boat in still waters is 10 km per hour then find the time taken to cover 60 kms downstream.

Solution: 

→ ATQ (According to Question) and formula given above:
→ 60/10+2 = 60/12 = 5 hours Answer.

Example 5.

Find the speed of the stream when a boat takes 5 hours to travel 60 kms downstream at a rate of 10 kms per hour in still water.

Solution: 

ATQ (According to Question) and formula given above:
→ Speed b + s = 60/5 = 12 kmph
→ Speed b = 10 kmph
→ So, speed s = 12-10 = 2 kmph Answer.

Example 6.

A boat covers a certain distance in one hour downstream with the speed of 10 kmph in still water and the speed of current is 4 kmph. Then find out the distance travelled.

Solution: 

ATQ (According to Question) and formula given above:
→ Distance = Speed x Time = 1 x (10+4) = 14 kms. Answer

Example 7.
A boat takes 6 hours to cover 36 km downstream and 8 hours to cover 32 km upstream. Then the speed of the boat in still water is?

Solution: 

ATQ (According to Question) and formula given above:
→ Speed of Boat = ½ (36/6 + 32/8) = ½ (6+4) = ½(10) = 5 kmph Answer.

Example 8.

A boat takes 6 hours to cover 36 km downstream and 8 hours to cover 32 km upstream. Then the speed of the stream is?

Solution: 

ATQ (According to Question) and formula given above:
Speed of Stream ½ (36/6 – 32/8) = ½ (6-4) = ½ (2) = 1 kmph Answer.

Example 9.

If a man rows 6 km downstream in 3 hours and 2 km upstream in 2 hours then how long will he take to cover 9 kms in stationary (still) water?

Solution: 

ATQ (According to Question) and formula given above:
→ Speed of Boat in still waters = ½ (6/3 + 2/2) = ½ (2 + 1) = 1.5 kmph
→ Time taken for 9 kms = 9/1.5 = 6 hours Answer
SBI PO Smart Prep Kit by Ramandeep Singh - Get here
notifications

Bank Exams Today Notes

Join 40,000+ readers and get free notes in your email

Let's block ads! (Why?)



- http://www.bankexamstoday.com/2017/03/shortcut-tricks-to-solve-boats-and.html
Shortcut Tricks to Solve Boats and Streams Questions 4.5 5 Yateendra sahu March 15, 2017 INTRODUCTION: Downstream: If the boat is moving in the direction of the stream. Upstream: If the boat is moving in the direction opposi...


Related Post:

  • Current Affairs Quiz : 25 March 2017
    SBI PO Smart Prep Kit by Ramandeep Singh - Get here Bank Exams Today Notes Join 40,000+ readers and get free notes in your email Let's block ads! (Why?) - http://www.bankexamstoday.com/2017/03/current-affairs-quiz-25-march-2017.html … Read More
  • Current Affairs: 26 March 2017
    Conference on 'Make in India' held in Houston First-ever conference was held here bringing together various constituencies that have an interest in India and discussing the latest developments and the best practices of doing business in India.&nbs… Read More
  • Banking & Financial Awareness One-Liner: March 2017
    BUDGETS IN VARIOUS STATES: Arunachal Pradesh Finance Minister presented the deficit budget of 285 crores.  Telangana Finance Minister presented the budget of rupees 1,49,646 crores for the year 2017-18.  Andhra Pradesh Government present… Read More
  • Reasons To Abolish Foreign Investment Promotion Board (FIPB)
    INTRODUCTION: The Foreign Investment Promotion Board (FIPB) is nothing but a national agency of Government of India, with the duty to consider & recommend foreign direct investment (FDI) that doesn’t come back beneath the automated route. … Read More
  • Tricks to Solve Surds and Indices Questions
    Ques 1:  Solve: 360.14 x 12960.18  Solution: Given that ab x ac = a (b+c) According to the question and as per the formula given above: 360.14 x 12960.18 (Make factors of 1296 = 36x36 i.e. equalizing the bases of the t… Read More
Load comments

No comments:

Post a Comment