A page is torn from a book. The sum of the remaining digits is 138. What are the page numbers on pag

M4maths Previous Puzzles

31 Jul 2020 Arithmetic

A page is torn from a book. The sum of the remaining digits is 138. What are the page numbers on page torn from this book?

OPtion

1) 9, 10
2) 8, 9
3) 10, 11
4) 11, 12
5) 13, 14
6) 12, 13
7) 7, 8
8) 14, 15
9) 15, 16
10) None of these

Solution

Let the total pages are 'n'. We have
1 + 2 + 3 + .........+n = 138
⇒ n(n+1) = 276
n (n+1) = 276
The square nearest to 276 is 289.This is the square of 17. Hence, we will take n= 17.
Therefore, sum of the pages= n(n+1)/2 = 17*18/2=153
Missing number = 153-138 =15.
Now, we have to think of 2 consecutive numbers whose sum is 15.
x+x+1=15 ⇒ ×= 7, 8

Correct Option: 7 Best Solution (5)

Devendra Marghade   4 years AGO

Sum of the pages of book of 17 pages=17*18/2=153
Given, sum of numbers of remaining pages=138
So, sum of the numbers of torn pages=153-138=15
Hence, the numbers on the pages torn are 7, 8
Option 7)

Like? Yes (2) | No (2)  

G.S.Kantharao   4 years AGO

No of pages is always even.
Hence total no.of pages are either 16 or 18.
Sum of 16=136
But it was given remaining is 138.
Then take 18. Sum of the numbers is 171
Given remaining as 138
Hence sum of the formed pages is 171-138=33
So the pages are 16,17
My option is 10✍️

Like? Yes (1) | No (2)  

susmitha   4 years AGO

n(n+1)/2 = 138
the near value for n(n+1)/2 could be 153
so, 153-138=15
where 7+8=15

Like? Yes (1) | No (2)  

Ravi kumar   4 years AGO

1+2+3+4+ ,+,+,+n = n(n+1)/2
Let 17
17(17+1)/2=153. More than 138. 153-138=15.
Then15 = 7+8

Like? Yes | No (2)  

RAMADURAI NATESAN   4 years AGO

No.of pages = 17. Sum =153.
Torn pages 7 and 8. 153 - 15 =138

Like? Yes | No (2)