Question 36 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards
Last updated at Oct. 27, 2020 by Teachoo
A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of the boat in still water and that of the stream.
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Question 36 A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of the boat in still water and that of the stream.Let the Speed of Boat in still water be x km/hr
& let the Speed of Stream be y km/hr
Now,
Speed Downstream = x + y
Speed Upstream = x β y
Given that
A boat goes 16 km upstream and 24 km downstream in 6 hours
Time taken to go 16 km upstream
+ Time taken to go 24 km downstream
(π·ππ π‘ππππ ππ 16 ππ)/(πππππ π’ππ π‘ππππ) + (π·ππ π‘ππππ ππ 24 ππ)/(πππππ πππ€ππ π‘ππππ) = 6
ππ/(π β π) + ππ/(π + π) = 6
We know that,
Speed = (π·ππ π‘ππππ )/ππππ
Time = (π·ππ π‘ππππ )/πππππ
Similarly,
A boat goes 12 km upstream and 36 km downstream in 6 hours
Time taken to go 12 km upstream
+ Time taken to go 36 km downstream
(π·ππ π‘ππππ ππ 12 ππ)/(πππππ π’ππ π‘ππππ) + (π·ππ π‘ππππ ππ 36 ππ)/(πππππ πππ€ππ π‘ππππ) = 6
ππ/(π β π) + ππ/(π + π) = 6
We know that,
Speed = (π·ππ π‘ππππ )/ππππ
Time = (π·ππ π‘ππππ )/πππππ
Our equations are
16(1/(π₯ β π¦))+24(1/(π₯ + π¦))=6 β¦(1)
12(1/(π₯ β π¦))+36(1/(π₯ + π¦))=6 β¦(2)
So, our equations become
Solving
16u + 24v = 6 β¦(3)
12u + 36v = 6 β¦(4)
Let 1/(π₯ β π¦) = u
1/(π₯ + π¦) = v
12u + 36v = 6
From (3)
16u + 24v = 6
16u = 6 β 24v
u = (6 β 24π£)/16
Putting value of u in (4)
12u + 36v = 6
12((6 β 24π£)/16)+36π£=6
3((6 β 24π£)/4)+36π£=6
Multiplying both sides by 4
4 Γ 3((6 β 24π£)/4)+"4 Γ" 36π£="4 Γ" 6
3(6 β 24v) + 144π£= 24
18 β 72v + 144v = 24
β 72v + 144v = 24 β 18
72v = 6
v = π/ππ
v = π/ππ
Putting v = 1/12 in equation (3)
12u + 36v = 6
12u + 36(1/12) = 6
12u + 3 = 6
12u = 6 β 3
12u = 3
u = 3/12
u = π/π
So, u = 1/4 & v = 1/12
But we need to find x & y
We know that
u = π/(π β π)
1/4 = 1/(π₯ β π¦)
x β y = 4
v = π/(π + π)
1/12 = 1/(π₯ + π¦)
x + y = 12
So, our equations become
x β y = 4 β¦(6)
x + y = 12 β¦(7)
Adding (6) and (7)
(x β y) + (x + y) = 4 + 12
2x = 16
x = 16/2
x = 8
Putting x = 8 in (7)
x + y = 12
8 + y = 12
y = 12 β 8
y = 4
So, x = 8, y = 4 is the solution of the given equation
Hence
Speed of boat in still water = x = 8 km/hr
Speed of stream = y = 4 km/hr
y = 12 β 8
y = 4
So, x = 8, y = 4 is the solution of the given equation
Hence
Speed of boat in still water = x = 8 km/hr
Speed of stream = y = 4 km/hr
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
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