given cho
A four-digit number, when successively divided by 6, 8 and 9, leaves remainders of 3, 2 and 1, respectively. What could be the remainder when the number is
divided by 108?
Only 99
Only 63
Only 27
99 or 63 or 27
Answers
Given : A four-digit number, when successively divided by 6, 8 and 9, leaves remainders of 3, 2 and 1, respectively.
To Find : What could be the remainder when the number is divided by 108?
Solution:
A four-digit number, when successively divided by 6, 8 and 9, leaves remainders of 3, 2 and 1,
N = 6A + 3
A = 8B + 2
B = 9C + 1
=> A = 8(9C + 1) + 2
=> A = 72C + 8 + 2
=> A = 72C + 10
=> N = 6 (72C + 10) + 3
=> N = 432C + 60 + 3
=> N = 432C + 63
=> N = 108 * 4C + 63
=> N = 108K + 63
Remainder would be 63 when Divided by 108
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