Question
What is least number which when successively divided by
6, 4 and 4 leaves a remainder 5, 3 and 3 respectively?Solution
ATQ,
First condition: N≡5(mod6). Let N=6a+5. Second condition: Quotient a≡3(mod4). Let a=4b+3. Substituting: N=6(4b+3)+5=24b+18+5=24b+23. Third condition: Quotient b≡3(mod4). Let b=4c+3. Substituting: N=24(4c+3)+23=96c+72+23=96c+95. Smallest N: Set c=0: N=96(0)+95=95. The least N is 95.
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