Decimalising The Remainders

A number when divided by 17 leaves 12 as remainder while on dividing by 11 leaves 8 as remainder.The remainder that it leaves on dividing by 23 is

In a question on division, the divisor is 6 times the quotient and 3 times the remainder. If the remainder is 40, then find the dividend.

What is the greatest number that will divide 99,123 and 183 leaving the same remainder in each case? Also, find the common remainder.

Remainder Theorem

The least number which on division by 35 leaves a remainder 25 and on division by 45 leaves the remainder 35 and on division by 55 leaves the remainder 45 is: