There are 25 trees at equal distances of 5 meters in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. The total distance the gardener will cover in order to water all the trees is

Question

There are 25 trees at equal distances of 5 meters in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. The total distance the gardener will cover in order to water all the trees is (A) 3550 m (B) 3434 m (C) 3370 m (D) 3200 m

Tardigrade Admin · Accepted Answer

Obviously the well (W) must be on one side of the trees

T_{1}, T_{2}, ......., T_{25}

,

The total distance covered by the gardener

= W T_{1} + (2 W T_{1} + T_{1} T_{2}) + (2 W T_{2} + T_{2} T_{3}) + ..... + (2 W T_{24} + T_{24} T_{25}]

= 10 + (2 \times 10 + 5) + (2 \times 15 + 5) + ............ +

to 25 terms

= 10 + (25 + 35 + 45 + ..........

to 24 terms )

= 10 + \frac{24}{2} [2 \times 25 + (24 - 1) \times 10]

= 10 + 12 [50 + 230] = 3370