GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Measured length $=285.5\mathit{m}$
Nominal length of tape $=30\mathit{m}$
Slope $=1$ in 10
The tape is $0.05\mathit{m}$ too short
Actual length of tape $=30-0.05=29.95\mathit{m}$
Actual length measured
Measured length
$=\frac{29.95}{30}\times 285.5$
$=285.024\mathit{m}$
Now slope correction $=\frac{-{\mathit{h}}^2}{2\mathit{L}}$
$\because$ Slope $=1$ in 10
$\Rightarrow \mathit{h}=\frac{1}{10}\times 285.024$
$\Rightarrow \mathit{h}=28.5024\mathit{m}$
⇒ Slope correction $=\frac{-{\left(28.5024\right)}^2}{2\times 285.024}$
$=-1.42512\mathit{m}$
$\Rightarrow$ Length to be plotted
$=$ Actual length measured + correction
$=285.024+\left(-1.42512\right)$
$=283.599\mathit{m}$
Hence, option (d) is correct.