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An airplane takes 1 hours less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.

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200

250

300

400

answer is C.

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Detailed Solution

Suppose usual speed of plane = x km/hr
It is know that,
Time= distance / speed
To cover 1200 km with x km/hr speed,

Time = \frac{1200}{x}

hr
New speed = (x+100) km/ hr
To cover 1200 km with (x+100) km/hr speed,

Time = \frac{1200}{x + 100}

hr
Now, time taken by airplane to cover 1200 km is 1 hours less when speed increased by 100 km/hr. So,

\frac{1200}{x} - \frac{1200}{100 + x} = 1

\frac{1200 (100 + x) - 1200 x}{x (100 + x)} = 1

120000 + 1200 x - 1200 x = (100 x + x^{2})

\Rightarrow 120000 = 100 x + x^{2}

\Rightarrow x^{2} + 100 x - 120000 = 0

(Quadratic equation)
Split the middle term

\Rightarrow x^{2} + 400 x - 300 x - 120000 = 0

\Rightarrow x (x + 400) - 300 (x + 400) = 0

\Rightarrow (x + 400) (x - 300) = 0

\Rightarrow x = - 400

and

x = 300

Value of speed cannot be equal to negative.
So, usual speed

x = 300 km / hr

Correct option is 3.

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