hi pooo...
here task is to find out the value of M such that 7M gives the remainder 8 on dividing by 12......
one way is hit 'n' trial......
another is the given one.....
ie....
if 7M is divided by 12 giving remainder 8, using remainder theorem,
let qoutient be 'a'.....
7M = 12a + 8.............................................(1)
=>7M = 5a +1 +7( a + 1 )
=>7M -7( a + 1 ) = 5a + 1
ie. 5a when divided by 7 gives remainder -1 or 6
again to find a way is hit 'n' trial or we know that 5a when divided by 7 gives rem 6
let quotient be 'b'......
ie. 5a = 7b + 6............................................(2)
=>5a - 5b - 5 = 2b + 1
ie. 2b when divided by 5 gives remainder -1 or 4
again to find a way is hit 'n' trial or we know that 2b when divided by 5 gives rem 4
let quotient be 'c'........
ie. 2b = 5c + 4.............................................(3)
=> 2b - 4c - 4 = c
=>2(b - 2c - 2) = c
i.e c is divisible by 2................
for least c = 0;
=> b = 2;....................from (3)
=>a = 4;.....................from(2)
=>M = 8;......................from (1)
therefore, D=17 using (1) that u have given..........
ie. 17th august..... |