Slove the problem..............................................
Answers
Answer: The correct answer is 451.
Step-by-step explanation:
It is given that sum of last 2 pages are 63.
∴ The two last pages are 31 and 32 since their sum is 63.
So the pages in the
(1) First half of the book are 1-16, &
(2) The second half 17-32.
He removed odd number of leaves in the first half (1 - smallest) and even number in second half (2-smallest).
To maximize the sum of whats left, he should be removing pages 1&2
from first half and pages 17,18,19 &20 from second half.
Total number of pages is (1+32)(16) = 528.
Subtracting the pages that were removed
528 - (1+2+17+18+19+20) = 451
Maximum Sum = 451.
Given:
The sum of the numbers of the pages on the last leaf of the book = 63
To Find :
We have to find the maximum possible sum of the numbers on the pages of leaves that were left in the book
Solution :
Let 'x' be the last page number on the last leaf.
Given that,
The sum of the numbers of the pages on the last leaf of the book = 63
x-1+x = 63
2x =64
x =32
⇒ Total number of leaves = = 16
∴ The book can be divided as follows :
- The first half from 1 to 16 ⇒ 8 leaves
- The second half from 17 to 32 ⇒8 leaves
On removing the pages, it is found that the number of leaves in the first case is odd and the second case is even. Also, we have to get the maximum possible sum of the numbers on the pages, so
→ Pages 1, 2 are removed from the first half ↔ One leaf ∵ odd
→ pages 17, 18, 19, 20 are removed from the second half ↔ Two leaves ∵ Even
∴ The sum of the remaining page numbers = Sum of the total number of page numbers - the sum of the removed page numbers
⇒ ( 1+2+3+4+...+32) - (1+2+17+18+19+20)
∴ The maximum possible sum of the numbers on the pages after removing = 451