Question

Doctor prescribed an old man to go regularly for a walk. He goes for some distance on first day but being on next day he goes half the distance. Similarly on each subsequent day he continues but goes only half the distances of previous day. The total distance moved by him can never exceed twice the distance moved by him on the first day.

• A. True
• B. False

Answer 1

The correct option is A True

Let he covered the distance on the first day be $x$.

But second day he covered $=\frac{x}{2}$

Third day he covered $=\frac{x}{4}$

And so on

Now, total distance covered by him

$S=x+\frac{x}{2}+\frac{x}{4}+\frac{x}{8}+........+\infty$

Hence, this is $G.P$

So,

$S=\frac{x}{1-\frac{1}{2}}$

$S=2x$

Hence, the total distance moved by him is twice the distance moved by him on the first day