The remainder is 20, when a number is divided by a divisor. If the remainder is 7 when thrice the original number is divided by the same divisor, find the value of the divisor.
Solution
Let us assume the number be 'x'.
Also, let us assume that the divisor is 'n'
Hence, x = n(a) + 20, where 'a' is the quotient ............ (1)
Also, 3x = n(b) + 7, where 'b' is the quotient ................(2)
Dividing (2) by (1), we get n (b-3a) = 53
Now, 53 is a prime number, and it can be broken into 53$$\times$$1.
Further, it is clear that the divisor cannot be 1, hence n = 53
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