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1. A minibus takes 6 hour less to cover 1680 km distance, if its speed is increased by 14 kmph ? What is the usual time of the minibus ?

A. 15 hours

B. 24 hours

C. 25 hours

D. 30 hours

Solution:

Let
Usual Speed = x kmph.
Now,
Speed of bus after increasing the speed = (x + 14)kmph. . . . . . . (1)
A ____________1680km ____________B
In first case,
Time taken to covered the distance 1680 km =

\frac{1680}{x}

. . . . . . . (2)
In Second Case,
Time Taken to covered the distance 1680 km =

\frac{1680}{x + 14}

Time difference = 6 Hours.
So,

\begin{aligned} \Rightarrow \frac{1680}{x} - \frac{1680}{x + 14} = 6 \\ \Rightarrow 1680 \frac{14}{x^{2} + 14 x} = 6 \\ \Rightarrow 280 \times 14 = x^{2} + 14 x \\ \Rightarrow x^{2} + 70 x - 56 x - 3920 = 0 \\ \Rightarrow x (x + 70) - 56 (x + 70) = 0 \\ \Rightarrow x = - 70, 56. \\ hence, speed of minibus is 56 k m / h \\ put x = 56 in equation (2) \\ T = \frac{1680}{56} \\ = 30 hours \end{aligned}

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