Suresh took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min, and Rajesh took the same time to cross the same field along its sides walking at the rate of 68 m/min. Find the area of the field.

Suresh took 15 seconds to cross the field diagonally at 52 m/min.

Rajesh took 15 seconds to cross the field along its sides at 68 m/min.

Let the sides of the rectangular field be x and y, and the diagonal be d.

From the Pythagorean theorem, d² = x² + y².

The area of the field = x × y.

Distance Suresh traveled diagonally in 15 seconds = (52/60) × 15 = 13 meters (diagonal)

Total distance Rajesh traveled along the sides in 15 seconds = (68/60) × 15 = 17 meters (perimeter of two sides).

Let the length and width of the field be x and y.

x + y = 17 (from Rajesh's distance), and diagonal = 13 (from Suresh's distance).

By using the Pythagorean theorem:

d² = x² + y² = 13² = 169

(x + y)² = x² + y² + 2xy = 17² = 289

169 + 2xy = 289

2xy = 120,

So, the area of the field (xy) = 60 m².

Thus, the area of the field is 60 m².

Correct option is  (b)