possible value of a+b for which 9 digit no.87a27931b is divisible by 11
Answers
Answer:
The possible value of a+b = 1 or 12
Step-by-step explanation:
Given,
The number is 87a27931b is divisible by 11.
Recall the concept
A number is divisible by 11, if
sum of digits at odd places - the sum of digits at even places = 0 or multiple of 11
Solution
Given number is 87a27931b
The sum of digits at odd places = b+3+7+ a+ 8 = 18+a+b
The sum of digits at even places = 1+9+2+7 = 19
Difference between the sum of digits at odd places - sum of digits at even places = 18+a+b - 19
Hence we have, 87a27931b is divisible by 11 if
either 18+a+b - 19 = 0 or 18+a+b - 19 is a multiple of 11
either a+b -1 = o or a+b -1 is a multiple of 11
Case 1
a+b -1 = 0
a+b = 1
Case 2
If a+b -1 is a multiple of 11
a+b = 12, 23,34,......
The only possible value of a+b in the above set is 12 because a and b are digits and the maximum possible value of a+b = 18
Hence, the number is 87a27931b is divisible by 11, if a+b = 1,or 12
∴The possible value of a+b = 1 or 12
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