Question

$30$ trees are planted in a straight line at intervals of $5m.$ To water them, the gardener needs to bring water for each tree, separately from a well, which is $10m$ from the first tree in line with the trees. How far will he have to walk in order to water all the trees beginning with the first tree? Assume that he starts from the first well, and he can carry enough water to water only one tree at a time.

• A. $4785m$
• B. $4795m$
• C. $4800m$
• D. None of these

Answer 1

Answer: (B)

$4795m$

To water the first tree he has to walk $=10$ metres

To water the second tree he has to walk $=25$ metres

To water the third tree he has to walk $=35$ metres

To water the fourth tree he has to walk $=45$ metres

So, if we observe the above distances except for the first they form an arithmetic progression,

$25,35,45,55,\dots \text{upto 29 terms}$

Let the total distance travelled by the gardener be $d.$ So,

$d=10+25+35+\dots$ to $30$ terms

$=10+(25+35+\dots 29\text{terms})$

$=10+\frac{29}{2}[2\times 25+(29-1)\times 10]$

$=10+\frac{29}{2}(50+28\times 10)$

$=10+4785$

$=4795m$

Hence, option $B$ is correct.