Question

25 trees are planted in a straight line at an interval of 5 metres. To water them the gardener must bring water for each tree separately from a well 10 metres from the first tree in line with the trees. Let $d$ be the distance he has to cover in order to water all the trees beginning with the first if he starts from the well.Find sum of digits of $d$?

Answer 1

Since the gardener starts from the well,

$\therefore$ Distance covered by gardener for water to first tree$D_1=O{A}_1=10$ metre.

Distance covered by gardener for water to second tree $D_2=A_{1}O+O{A}_2=10+15=25$ metre.

Distance covered by gardener for water to third tree $D_3=A_{2}O+O{A}_3=15+20=35$ metre.

Distance covered by gardener for water to fourth tree $D_4=A_{3}O+O{A}_4=20+25=45$ metre.

Hence, distance covered by the gardener for water to all the trees

$D=10+25+35+45+...to25$ trees

$=10+(25+35+45+...to24$ trees

$=10+\frac{24}{2}\{2.25+(24-1\left)10\right\}$

$=10+12\{50+230\}$

$=10+12.280$

$=10+3360=3370$ metre

Sum of the digits of d- 3+3+7= 13