A farmer moves along the boundary of a square field of side 10 m in 40 s.

First we will convert the time into seconds

 Total time = 2 minutes 20 seconds

 = 2× 60 seconds + 20 seconds

 = 120 seconds + 20 seconds

 = 140 seconds

Now, If in 40 s,

Number of rounds made = 1

So, In 140 sec the number of rounds made

= 1/40×140

= 3.5 rounds

Thus, the farmer will make 3.5 rounds of the square field.

If the farmer starts from position A (see figure), then after three complete rounds, he will reach at starting position A.

But in the next half round, the farmer will move from A to B, and B to C, so that his final position will be at C.

Hence, the total displacement of the farmer will be AC.

Now, ABC is a right angled triangle with AC as hypotenuse.

 So,

 (AC)² = (AB)² + (BC)²

(AC)² = (10)² + (10)²

(AC)² = 100 + 100

(AC)² = 200

 AC = 14.143 m

Hence, the magnitude of displacement of the farmer at the end of 2 minutes and 20 seconds will be 14.143 metres.