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Standard VIII

Mathematics

Solving an Equation with Variables on Both Sides

A boat takes ...

Question

A boat takes 11 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream be 3 km/hr and the speed of the boat in still water be `12 km/hr, then what is the distance between A and B ?

100

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90

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110

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120

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Solution

The correct option is B $90$ km
Speed of downstream = (12 + 3) km/hr = 15 km/hr
Speed upstream = ( 12 - 3) km/hr = 9 km/hr
Let the distance between A and B be x km. Then,
$\frac{x}{15} + \frac{\frac{x}{2}}{9} = 11 \Rightarrow \frac{x}{15} + \frac{x}{18} = 11$
$\Rightarrow \frac{6 x + 5 x}{90} = 11 \Rightarrow \frac{11 x}{90} = 11 \Rightarrow x = 90 k m$

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A boat takes 11 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream be 3 km/hr and the speed of the boat in still water be `12 km/hr, then what is the distance between A and B ?

The correct option is B 90 kmSpeed of downstream = (12 + 3) km/hr = 15 km/hrSpeed upstream = ( 12 - 3) km/hr = 9 km/hrLet the distance between A and B be x km. Then, x15+x29=11⇒x15+x18=11⇒6x+5x90=11⇒11x90=11⇒x=90km