question_answer

A rectangular field is 112 m long and 100 m wide. Two roads, each 3 m wide are to be constructed at the centre of this field; one is parallel to the length of the field and the other is parallel to the breadth of the field.        Find:                                   

(i) Area of the part of the field, not covered by the roads.

(ii) Cost of constructing the road at Rs.17 per\[{{m}^{2}}\].

           

A)

(i)	(ii)
\[3248\,{{m}^{2}}\]	Rs.2890

               

B)

(i)	(ii)
\[10573\,{{m}^{2}}\]	Rs.10659

               

C)

(i)	(ii)
\[16582\,{{m}^{2}}\]	Rs.20480

               

D)

(i)	(ii)
\[10573\,{{m}^{2}}\]	Rs.1250

Correct Answer: B

Solution :

                                        (i) Area of path BSTV\[~=100\times 3=300\text{ }{{m}^{2}}\] Area of path MNDP \[=112\times 3=336\text{ }{{m}^{2}}\] \[\therefore \] Total area of two paths \[=(300+336)-\] Area of square HGFE \[=636-3\times 3=627\text{ }{{m}^{2}}\] \[\therefore \] Area of field not covered by roads = Total area of field - Area of two paths \[=(112\times 100)-627=10573\,{{m}^{2}}\] (ii) Cost of constructing \[1\text{ }{{m}^{2}}\]area = Rs. 17 \[\therefore \]Cost of constructing the roads             \[=Rs.\,(17\times 627)=Rs.\,10659\]