A low-lying plot of land measuring 48 meters in length and 31.5 meters in width is to be raised by 6.5 decimeters. To achieve this, a nearby pit measuring 27 meters in length and 18.2 meters in width is dug. What will be the depth of the pit?

Q.A low-lying plot of land measuring 48 meters in length and 31.5 meters in width is to be raised by 6.5 decimeters. To achieve this, a nearby pit measuring 27 meters in length and 18.2 meters in width is dug. What will be the depth of the pit?

Let the depth of the pit be \(d\) meters. ∴ Volume of soil dug from the pit = \(27 \times 18.2 \times d\) cubic meters Now, the low-lying land is to be raised by 6.5 decimeters = 0.65 meters ∴ According to the question: \[ 27 \times 18.2 \times d = 48 \times 31.5 \times 0.65 \Rightarrow d = \frac{48 \times 31.5 \times 0.65}{27 \times 18.2} \Rightarrow d = 2 \] ∴ The pit must be 2 meters deep