Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2006 · Marks: · Difficulty:
A plot of land in the form of a rectangle has dimensions 240 m × 180 m. A drainlet 10 m wide is dug all around it (outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. The depth of the drainlet is
(a)1.223 m
(b)1.225 m
(c)1.227 m
(d)1.229 m
Answer
Answer (as printed): C
Explanation
Volume of earth dug out $=(240 \times 180 \times 0.25) \mathrm{m}^{3}$ $$=10800 \mathrm{m}^{3} .$$ Let the depth of the drainlet be $h$ metres. Then, volume of earth dug out $$\begin{aligned} & =[\{(260 \times 200)-(240 \times 180)\} h] \mathrm{m}^{3}=(8800 h) \mathrm{m}^{3} . \\ \therefore 8800 h & =10800 \Rightarrow h=\frac{10800}{8800}=\frac{27}{22}=1.227 \mathrm{m} . \end{aligned}$$