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Class 10
>>Maths
>>Pair of Linear Equations in Two Variables
>>Algebraic Methods of Solving a Pair of Linear Equations
>>A boat goes 15km upstream and 22km down
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A boat goes 15km upstream and 22km down stream in 15 hours. In 14 hours it can go 45 upstream and 55km down stream. The speed of the boat in still water in km/hr is
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Solution
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Correct option is D)
Let speed of boat in still water(in km/hr) =x and speed of stream(in km/hr) =y
Time required by the boat to travel d kilometers upstream is
x−y
d
.
Time required by the boat to travel d kilometers downstream is
x+y
d
.
According to the given condition,
x+y
22
+
x−y
15
=5
And
x+y
55
+
x−y
45
=14
Here only x is to be found so option method cannot be used using substitution method
Let
x+y
1
=u,
x−y
1
=v
22u+15v−5=0
55u+45v−14=0
Then, by cross multiplication
−15×14−(45)×−5
u
=
−5×55−22×(−14)
v
=
22×45−55(15)
1
−210+225
u
=
−275+308
v
=
990−825
1
15
u
=
33
v
=
165
1
u=
11
1
,v=
5
1
x+y=11, x−y=5
Add both the equations.
⇒ 2x=16
⟹x=8
Explanation:
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