in the given region a total of 9 regions are formed by 5 circles. three such regions represented by numbers 12,6 and 15. use any other numbers once only for rest of regions so that sum of numbers in each circle is 20.
Answers
Given:-
- Total number of regions are 9.
- Three regions represented by numbers 12, 6 and 15.
To Find:-
- The number through which we have to represent remaining regions.
Rule:-
- Use any number under 20 except 12, 6 and 15.
- Use any number only once.
- Represent the number such that sum of the circle including region/regions is 20.
Solution:-
Here, The First region is represented by the number 12.
20 - 12 = 8
Hence, the 2nd region is represented by the number 8.
Now, The 9th region is represented by the number 15.
20 - 15 = 5
Hence, the 8th region is represented by the number 5.
Since, Sum of 6th, 7th and 8th region will be 20.
Therefore, 5 + 6th + 7th = 20
6th + 7th = 15
Now, Let's take a number that is 13.
13 + 7th = 20
7th = 7
Hence, 6th and 7th region will be represented by the number 13 and 7 respectively.
Since, 5th region is represented by the number 6.
So, 4th + 5th + 6th = 20
⇒ 4th + 6 + 13 = 20
⇒ 4th = 1
Hence, 4th region is represented by the number 1.
Now, 2nd and 4th region is represented by the number 8 and 1 respectively.
So, 2nd + 3rd + 4th = 20
⇒ 8 + 3rd + 1 = 20
⇒ 3rd = 11
Therefore, 1st region = 12
2nd region = 8
3rd region = 11
4th region = 1
5th region = 6
6th region = 13
7th region = 7
8th region = 5
9th region = 15