In crossing a distance of $30$km. A takes $2$hrs more than B. If A double his speed , he wo have taken $1$ hr less than B. Then trir speeds are

Let the speed of A be x km/hr and the speed of B be y km/hr. Using the formula Time equals Distance divided by Speed, the first condition gives 30/x minus 30/y equals 2, which simplifies to 15(x minus y) equals xy. The second condition gives 30/(2x) minus 30/y equals negative 1, or 15/x minus 30/y equals negative 1, simplifying to 15(y minus 2x) equals negative xy. Equating the two expressions for xy yields 15x minus 15y equals 15y minus 30x, meaning 45x equals 30y and y equals 1.5x. Substituting this into the first equation gives 15(0.5x) equals 1.5(x squared), so x equals 5. This means the speeds are 5 km/hr and 7.5 km/hr.

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