1.

A man reduces his speed to two-third to walk a distance and consequently becomes late by 1 hour. With his usual speed, he covers the same distance in (a) \(\frac14\) hour (b) \(\frac12\) hour (c) 2 hours(d) \(1\frac12\) hours

Answer»

(c) 2hrs

Let the distance to be covered be x km at y km/hr.

∴ \(\frac{x}{y}=\frac{x}{\frac23y}-1\) ⇒ \(\frac{x}{y}-\frac{3x}{2y}=-1\) ⇒ \(\frac{2x-3y}{2y}=-1\)

⇒ –x = – 2y ⇒ x = 2y. 

∴ With his usual speed the time taken to cover a distance x km. = \(\frac{x}{y}=\frac{2y}{y}\) hrs = 2hrs.


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