# Aptitude - Boats and Streams - Discussion

Discussion Forum : Boats and Streams - General Questions (Q.No. 4)

4.

A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Answer: Option

Explanation:

Let the speed of the stream be *x* km/hr. Then,

Speed downstream = (15 + *x*) km/hr,

Speed upstream = (15 - *x*) km/hr.

30 | + | 30 | = 4 | 1 | |

(15 + x) |
(15 - x) |
2 |

900 | = | 9 | |

225 - x^{2} |
2 |

9*x*^{2} = 225

*x*^{2} = 25

*x* = 5 km/hr.

Video Explanation: https://youtu.be/lMFnNB3YQOo

Discussion:

63 comments Page 1 of 7.
Likitha Ganta said:
10 months ago

Speed in still water = 15 km/hr.

Distance traveled in downstream = 30 km.

Time taken in upstream = 4 hr 30 min.

The speed of the stream = ?

Speed = Distance/time.

Distance = 30km.

Speed in upstream = (u-v)km/hr = (15-v)km/hr.

Speed in downstream = (u+v)km/hr = (15+v)km/hr.

Total time = (distance of downstream/speed of downstream) + (distance of upstream/speed of upstream).

30/(15 + x) + 30/(15 - x) = 4 1/2,

30/(15 + x) + 30/(15 - x) = 9/2,

30(15 - x) + 30(15 + x) = 9/2 * (15 - x)(15 + x),

900 = 9/2 * (225 + 15x - 15x - x^ 2),

900 = 9/2 * (225 - x ^ 2),

1800= 9(225 - x ^ 2),

1800 = 2025 - 9x ^ 2,

2025 - 1800 = 9x ^ 2,

225 = 9x ^ 2,

x ^ 2 = 225/9 = 25,

x = √(25) = 5.

Ans=>X=5.

Distance traveled in downstream = 30 km.

Time taken in upstream = 4 hr 30 min.

The speed of the stream = ?

Speed = Distance/time.

Distance = 30km.

Speed in upstream = (u-v)km/hr = (15-v)km/hr.

Speed in downstream = (u+v)km/hr = (15+v)km/hr.

Total time = (distance of downstream/speed of downstream) + (distance of upstream/speed of upstream).

30/(15 + x) + 30/(15 - x) = 4 1/2,

30/(15 + x) + 30/(15 - x) = 9/2,

30(15 - x) + 30(15 + x) = 9/2 * (15 - x)(15 + x),

900 = 9/2 * (225 + 15x - 15x - x^ 2),

900 = 9/2 * (225 - x ^ 2),

1800= 9(225 - x ^ 2),

1800 = 2025 - 9x ^ 2,

2025 - 1800 = 9x ^ 2,

225 = 9x ^ 2,

x ^ 2 = 225/9 = 25,

x = √(25) = 5.

Ans=>X=5.

(3)

Saji said:
2 years ago

(30/15+x) + (30/15-x) =4 (1/2).

By cross multiplying;

(30(15-x) + 30(15+x)) /(15+x) (15-x) = 9/2.

(450-30x+450+30x)/15^2 - x^2 = 9/2.

-30x and +30x get cancelled.

So,

900/15^2 -x^2 = 9/2.

By cross multiplying;

(30(15-x) + 30(15+x)) /(15+x) (15-x) = 9/2.

(450-30x+450+30x)/15^2 - x^2 = 9/2.

-30x and +30x get cancelled.

So,

900/15^2 -x^2 = 9/2.

(5)

Gayu said:
2 years ago

Someone help me to understand the solution, please.

(2)

Anjali said:
4 years ago

As we have given upstream speed=15 from option lets take 4 so for,

Downstream 15 + 4 = 19 and upstream 15 -4 = 11.

The distance is given so 30/19=1.58 and 30/11=2.72 it not satisfy condition so take next option

as 5 so similarly 15 +5 = 20 and 15 - 5 =10 so 30/20 = 1.5 and 30/10 = 4.

So 1.5 +4 = 4.5 and our time is also 4.5 so the answer is 4.5.

Downstream 15 + 4 = 19 and upstream 15 -4 = 11.

The distance is given so 30/19=1.58 and 30/11=2.72 it not satisfy condition so take next option

as 5 so similarly 15 +5 = 20 and 15 - 5 =10 so 30/20 = 1.5 and 30/10 = 4.

So 1.5 +4 = 4.5 and our time is also 4.5 so the answer is 4.5.

(9)

Tanu said:
5 years ago

Motorboat goes down stream 30 kilometre and again returns to the starting point from a total time of 4 hours and 30 minutes if the speed of the stream is 5 kilometre per hour then find the speed of the motor boat in still water please solve this.

(1)

Balu said:
5 years ago

Speed in still water = 15 km/hr.

Distance traveled in downstream = 30 km.

Time taken in upstream = 4 hr 30 min.

The speed of the stream = ?

Speed = Distance/time.

Distance = 30km.

Speed in upstream = (u-v)km/hr = (15-v)km/hr.

Speed in downstream = (u+v)km/hr = (15+v)km/hr.

Total time = (distance of downstream/speed of downstream) + (distance of upstream/speed of upstream).

(30/(15+v))+(30/(15-v)) = 4 1/2.

(30(1/(15-v))+(1/(15+v)) = 4 1/2.

(30((15+v)+(15-v))/(15+v)(15-v))=9/2

(30(15+15+v-v)/(15^2-v^2))

30*30/225-v2=9/2

900/(225 - v^2) = 9/2

900 / (225 - v^2) = 9/2.

900 * 2 = 9(225 -v^2).

1800 = 2025 - 9v^2.

9v^2 = 2025 - 1800.

9v^2 = 225.

v^2 = 225/9.

v^2 = 25.

v = 5 Km/hr.

Distance traveled in downstream = 30 km.

Time taken in upstream = 4 hr 30 min.

The speed of the stream = ?

Speed = Distance/time.

Distance = 30km.

Speed in upstream = (u-v)km/hr = (15-v)km/hr.

Speed in downstream = (u+v)km/hr = (15+v)km/hr.

Total time = (distance of downstream/speed of downstream) + (distance of upstream/speed of upstream).

(30/(15+v))+(30/(15-v)) = 4 1/2.

(30(1/(15-v))+(1/(15+v)) = 4 1/2.

(30((15+v)+(15-v))/(15+v)(15-v))=9/2

(30(15+15+v-v)/(15^2-v^2))

30*30/225-v2=9/2

900/(225 - v^2) = 9/2

900 / (225 - v^2) = 9/2.

900 * 2 = 9(225 -v^2).

1800 = 2025 - 9v^2.

9v^2 = 2025 - 1800.

9v^2 = 225.

v^2 = 225/9.

v^2 = 25.

v = 5 Km/hr.

(11)

Monika said:
6 years ago

Thank you all for giving the answer.

(3)

Basavaraju H K said:
6 years ago

30/(15+x)+30/(15-x)=4 1/2.

Don't multiply take LCM then it will be;

{ 30(15- x)+30(15+x)}/(15+x)(15-x) = 4 1/2.

450-30x+450+30x /(15+x) (15 - x) = 9/2.

-30x+30x will be cancelled then;

900 /15^2-x^2=9/2.

**(a+b)(a-b)=a^2-b^2 **

When cross multiplied we get;

2 * 900=9(15^2-x^2),

1800=2025-9x^2 so,

9x^2=2025-1800,

9x^2=225,

x^2=225/9,

x^2=25,

x = 5.

Don't multiply take LCM then it will be;

{ 30(15- x)+30(15+x)}/(15+x)(15-x) = 4 1/2.

450-30x+450+30x /(15+x) (15 - x) = 9/2.

-30x+30x will be cancelled then;

900 /15^2-x^2=9/2.

**(a+b)(a-b)=a^2-b^2 **

When cross multiplied we get;

2 * 900=9(15^2-x^2),

1800=2025-9x^2 so,

9x^2=2025-1800,

9x^2=225,

x^2=225/9,

x^2=25,

x = 5.

(3)

Disha said:
6 years ago

@All.

x=consider speed of boat , which is 15kmph.

d=30km.

t=4hr30 min.

Given in question that it comes back, means the boat has taken a lap .so it will be one time upstream and second downstream. That is why both x+y and x-y has been taken.

30/(x+y)+30/(x-y)=9/2.

x=5.

x=consider speed of boat , which is 15kmph.

d=30km.

t=4hr30 min.

Given in question that it comes back, means the boat has taken a lap .so it will be one time upstream and second downstream. That is why both x+y and x-y has been taken.

30/(x+y)+30/(x-y)=9/2.

x=5.

(3)

Geetha said:
6 years ago

How 900 came? Explain.

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