A took 15 sec to cross a rectangular field diagonally walking at the rate of speed 52 m/min and B took the same time to cross the same field along its sides walking at the rate speed 68 m/min. The area of the field is:

Solution (By Examveda Team)

BD = length of diagonal = speed × time
$$\eqalign{ & = \frac{{52}}{{60}} \times 15 \cr & = 13{\text{ m}} \cr & {\text{BD}} = \sqrt {{l^2} + {b^2}} \cr & \Rightarrow {l^2} + {b^2} = {13^2} \cr & \Rightarrow {l^2} + {b^2} = 169 \cr & {\text{Again, }}l + b = \frac{{68}}{{60}} \times 15 = 17 \cr & {\left( {l + b} \right)^2} = {l^2} + {b^2} + 2lb \cr & {17^2} = 169 + 2lb \cr & lb = \frac{{120}}{2} = 60{\text{ }}{{\text{m}}^2} \cr} $$