A boy walked along two adjacent sides of a rectangular field. If he had walked along the diagonal,then he would have saved a distance equal to one-fourth of the larger side. The ratio of the larger to the smaller side is:

Let the length, breadth and diagonal of rectangle is l, b and d respectively as shown in figure below : 

As we know, 

Length of rectangle is always greater than breadt.

l, b and d always follow the pythagoras relation,

i.e, $$d^2=l^2+b^2$$.................(i)

According to question, 

$$l+b-d=\frac{1}{4}\times\ l$$

$$\frac{3l}{4}+b=d$$.................(ii)

Putting the value of d from (ii) into (i)

$$\left(\frac{3l}{4}+b\right)^2=l^2+b^2$$

$$\therefore\ \frac{9l}{16}+b^2+\frac{3l}{2}=l^2+b^2$$

$$\therefore\ l^2-\frac{9l^2}{16}=\frac{3lb}{2}$$

$$\therefore\ l-\frac{9l}{16}=\frac{3b}{2}$$

$$\therefore\ \frac{7l}{16}=\frac{3b}{2}$$

$$\therefore\ \frac{l}{b}=\frac{24}{7}$$

So, Require Ratio = 24 : 7

Hence, Option C is correct.