Question

Four horses are tied on the four corners of a square field of $14m$ length so that each horse can just touch the other two horses. They ware able to graze in the area accessible to them for $11$ days. For how many days is the ungrazed area sufficient for them?

• A. $3$ days
• B. $4$ days
• C. $5$ days
• D. $2$ days

Answer 1

The correct option is C $5$ days

As each horse is able to touch other, the length of rope $=7m$

Each horse is able to graze the area equals to sector of radius $7m$ and angle $90$ degree.

$4$ horses will able to graze the area equal to circle of $7m$ radius (as four sector of $90$ degree each combines to form circle of radius $7m$)

Hence, area of circle $=7\times 7\times \frac{22}{7}=154m^2$

Area of square $=14\times 14=196m^2$

Remaining area to graze $=196-154=42m^2$

$154$ sq. m can be grazed by horses in $11$ days.

Thus, $42m^2$ can be grazed by horses in $3$ days.