A takes 3 hours more than B to walk 'd' km. If A doubles his speed, then he can make it in 1 hour less than B. How much time (in hours) does A require to walk 'd' km?

Solution (By Examveda Team)

Let the speed of the A be a and B be b
According to the question,
$$\frac{{\text{d}}}{{\text{a}}} - \frac{{\text{d}}}{{\text{b}}} = 3 - - - - \left( {\text{i}} \right)$$
Again,
$$\frac{{\text{d}}}{{\text{b}}} - \frac{{\text{d}}}{{2{\text{a}}}} = 1 - - - - \left( {{\text{ii}}} \right)$$
By adding equation (i) and (ii) we get,
$$\eqalign{ & \frac{{\text{d}}}{{2{\text{a}}}} = 4 \cr & \Rightarrow \frac{{\text{d}}}{{\text{a}}} = 4 \times 2 \cr & \Rightarrow \frac{{\text{d}}}{{\text{a}}} = 8 \cr} $$
So, it will take 8 hours by A to cover the distance d
∴ A requires 8 hours to walk 'd' km.