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in Road Safety Education by (35.3k points)
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Some vehicles are parked in no parking zone on a road, in which 10 m distance is maintained between each vehicles. A larger vehicle (truck) of municipality is standing in middle of the place. Crane can load one vehicle into larger truck in a single time. Total number of vehicles on the road is add excluding crane. At last crane covers a distance of 3 km. Find the total number of vehicle including crane.

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Best answer

Let total vehicles on road excluding crane = 2n + 1.

Vehicles on both sides of larger vehicle = n + n.

Distance covered in lifting vehicles by crane between P and M.

Sn = 10n + 2[10(n – 1) + 10(n – 2) + ………..+10 × 2 + 10 × 1]

Similar, Distance covered in lifting vechiles between Q and M.

Sn = 2[10n + 10(n – 1) + 10(n – 2) + ………+10 × 2 + 10 × 1]

Total distance covered

S = Sn + Sn

∵ Since crane covered 3000 m (3 km) distance in total.

∴ 20n2 + 10n = 3000

⇒ 2n2 + n – 300 = 0

⇒ (n – 12)(2n + 25) = 0

∵ n ≠ -ive

n – 12 = 0

∴ 2n + 1 = 2 × 12 + 1 = 25

Hence, there, are total 26(25 + 1) vehicles including crane.

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