AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A boat goes 16 km upstream and 24 km downstream in 6 hours. Also, it covers 12 km upstream and 36 km downstream in the same time. Find the speed of the boat in still water and that of the stream.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Boat

= 8 km / hr

and

Stream = 4 km / hr

Boat

= 3 km / hr

and Stream

= 4 km / hr

Boat

= 9 km / hr

and Stream

= 4 km / hr

Boat

= 4 km / hr

and Stream

= 4 km / hr

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

It is given that,
Boat goes 16 km upstream and 24 km downstream in 6 hours and it covers 12 km upstream and 36 km downstream in the same time.
Let the stream's speed be

y km / hr

and the boat's speed in still water be

x km / hr

.
Therefore,
Speed upstream = (x – y) km/hr
Speed downstream = (x + y) km/hr.
According to question,
Time taken to cover 16 km upstream =

16 (x - y) hr

.
Time Taken to cover 24 km downstream =

24 (x + y)

hr.
Total Time Taken to cover both distance = 6 hr.
Therefore,

16 (x - y) + 24 (x + y) = 6

.…... (1)
And
Time taken to cover 12 km upstream =

12 (x - y)

hr.
Time Taken to cover 36 km downstream =

36 (x + y)

hr.
Total Time Taken to cover both distance = 6 hr.
Therefore,

12 (x - y) + 36 (x + y) = 6

.…... (2)
Putting

1 x − y = u and 1 x + y ​ ​ ​ ​ = v

.
Then the equations become,

16 u + 24 v = 6 … … . 3 12 u + 36 v = 6 … … . 4

Multiplying equation (3) by 4 and equation (4) by 3,

48 u + 72 v = 18 … … . 5 48 u + 144 v = 24 … … . 6

Subtracting equation (5) from equation (6), we get:

v = \frac{1}{12}

Using the value of

v

to solve equation (4) will yield the value of u,

12 u + 36 v = 6 12 u + 36112 = 6 12 u + 3 = 6 12 u = 6 − 3 12 u = 3 u = 312 u = 14

Put the value of u and v in

1 x − y = u and 1 x + y ​ ​ ​ ​ = v

we get,

1 x − y = 14 and 1 x + y ​ ​ ​ ​ = 112

So,

1 x − y = 14 ⇒ x − y = 4 ... (7) and 1 x + y ​ ​ ​ ​ = 112 ⇒ x + y = 12 ... (8)

From equations (7) and (8) we get,

x = 8 and y = 4

So, the speed of the boat in still water is 8km/hr and the speed of the stream is 4km/hr.
Hence, option (1) is correct.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

best study material, now at your finger tips!

live classes
progress tracking
24x7 mentored guidance
study plan analysis

download the app

A boat goes 16 km upstream and 24 km downstream in 6 hours. Also, it covers 12 km upstream and 36 km downstream in the same time. Find the speed of the boat in still water and that of the stream.

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App