A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to:

Solution(By Examveda Team)

Let A's speed = x km/hr
Then, B's speed = (7 - x) km/hr
So,
$$\eqalign{ & \Leftrightarrow \frac{{24}}{x} + \frac{{24}}{{\left( {7 - x} \right)}} = 14 \cr & \Leftrightarrow 24\left( {7 - x} \right) + 24x = 14x\left( {7 - x} \right) \cr & \Leftrightarrow 14{x^2} - 98x + 168 = 0 \cr & \Leftrightarrow {x^2} - 7x + 12 = 0 \cr & \Leftrightarrow \left( {x - 3} \right)\left( {x - 4} \right) = 0 \cr & \Leftrightarrow x = 3{\text{ or }}x = 4 \cr} $$
Since A is faster than B,
So, A's speed = 4 km/hr
And B's speed = 3 km/hr