A monkey ascends on a pole he ascends 5/2 m in first minute and slips down 3/2 metres in the next other minute . in how much time will the monkey reach at the top of the pole of 21/2 m height
Answers
Topic
Application of Operators
Given
A monkey ascends on a pole, he ascends 2.5 metres in first minute and slips down 1.5 metres in the next other minute.
To Find
Time taken by monkey to reach at the top of pole which is 10.5 metres high.
Concept
We need to add 2.5 metres while considering monkey has climbed up and subtract 1.5 metres while considering monkey has slipped down.
We need to do it until monkey reaches at the top of pole means we have to do it until the sum of distances climbed up is equal to 10.5 metres.
Solving
Distance ascended by monkey in :-
1st Minute
2.5 metres
2nd Minute
( 2.5 - 1.5 ) metres
1 metres
3rd Minute
( 1 + 2.5 ) metres
3.5 metres
4th Minute
( 3.5 - 1.5 ) metres
2 metres
5th Minute
( 2 + 2.5 ) metres
4.5 metres
6th Minute
( 4.5 - 1.5 ) metres
3 metres
7th Minute
( 3 + 2.5 ) metres
5.5 metres
8th Minute
( 5.5 - 1.5 ) metres
4 metres
9th Minute
( 4 + 2.5 ) metres
6.5 metres
10th Minute
( 6.5 - 1.5 ) metres
5 metres
11th Minute
( 5 + 2.5 ) metres
7.5 metres
12th Minute
( 7.5 - 1.5 ) metres
6 metres
13th Minute
( 6 + 2.5 ) metres
8.5 metres
14th Minute
( 8.5 - 1.5 ) metres
7 metres
15th Minute
( 7 + 2.5 ) metres
9.5 metres
16th Minute
( 9.5 - 1.5 ) metres
8 metres
17th Minute
( 8 + 2.5 ) metres
10.5 metres
So, monkey reaches at the top of Pole in 17 minutes.
Technique 2
We can observe that monkey ascends 1 metre in 2 minutes.
So,
Monkey will cover 8 metres in
8 × 2 minutes = 16 minutes
and
In 17th minute, monkey will ascend
( 8 + 2.5 ) metres
10.5 metres.
Answer
So, monkey will reaches at the top of Pole in 17 Minutes.
Distance travelled in 2 minutes=3−1=2 metres, i.e. 1 metre in one minute.Let us suppose that he ascends 3 m. at the last minute, so that he covers the 9 metres at the rate of 1 metre in 1 minute in 9 minutes..Thus, he will reach the top in 10th minute.