A) 3
B) 5
C) 8
D) 10
Correct Answer: C
Solution :
[c] Since speed of bus increases every hour by 3 km/hr. \[\therefore \] Initial speed =21 km/hr Total distance = 252 km According to Arithmetic Progression a=21, d=3, Sn = 252n=? \[{{S}_{n}}=\frac{n}{2}([2a+(n-\,1)d])\] \[252=\frac{n}{2}(42+3n-\,3)\] \[504=n\,(3n+39)\] \[3{{n}^{2}}+39n-\,504=0\] \[{{n}^{2}}+21n-\,8n-\,168=0\] \[\Rightarrow n\,\,(n+21)-8\,\,(2+21)=0\] \[\therefore (n-8)\,\,(n+21)\] \[\Rightarrow n=8,\,\,n\ne -21\] \[\therefore \]So, 8 hours will it take to cover a distance of 252 km
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