Question

Arun can climb a Coconut tree by 1.5 feet by each lift; however he slips 0.5 feet every time he makes the next lift. How many individual lifts he will have to make, to reach the top of the Coconut tree of 18.5 feet?
$
  {\text{A}}{\text{. 20}} \\
  {\text{B}}{\text{. 19}} \\
  {\text{C}}{\text{. 18}} \\
  {\text{D}}{\text{. 17}} \\
$

Answer 1

Hint: In order to find the number of lifts to be taken to reach the top of the tree of 18.5 feet, we calculate the aggregate increase of height of arun per lift. Then we compute the number of lifts needed to climb the top of the tree.

Complete step-by-step answer:
Given data,
Arun climbs 1.5 feet per each lift, but drops 0.5 feet when he makes the next lift.
Height of tree = 18.5 feet

Arun climbs 1.5 feet for every lift and drops 0.5 feet in the next lift.
So the aggregate height gained by arun per step is given by
1.5 – 0.5 = 1 feet
So arun gains an aggregate of 1 feet for every single lift.

The height of the tree is 18.5 feet.

So for 17 lifts, arun gains an aggregate height of
1 × 17 = 17 feet.
In the eighteenth lift, Arun gains a lift of 1.5 feet as everytime.
By the 18th lift, the total height reached by arun = 17 + 1.5 = 18.5 feet
Arun does not need to take any more lifts.
Therefore, Arun reached the top of the tree by the 18th lift.

The number of individual lifts he will have to make, to reach the top of the Coconut tree of 18.5 feet is 18.

Option C is the correct answer.

Note: In order to solve this type of questions the key is to consider the gain and loss of height and calculate the net gain of height per lift. This helps us calculate the height gained for any number of lifts.
We stopped calculating the net gain of height at 17th lift, keeping in mind that he just needs to gain 1.5 feet more and he would do that in the 18th step because he need not try to take a 19th lift, as he already reached the top.