The sleeper density is M + 7 on a broad-gauge route, where M is the length of the rail. How many sleepers are required for 1 km length of track?
(Assume the length of the rail is 13 m)
DSSSB JE - 2023,
Answer: C
The sleeper density is M + 7 per rail length, where M is the length of the rail in metres, so for a 13 m rail the density is 13 + 7 = 20 sleepers per rail. The number of rail lengths in a kilometre is 1000/13 = 76.92, so
\[ \begin{aligned} N = 76.92 \times 20 \\ &= 1538.5 \approx 1539\ \text{sleepers} \end{aligned} \]The values 1510, 1520 and 1525 would result from rounding the number of rails down before multiplying or from a slightly different density.
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