Question

1MN ÷ 3 = MN, Replace the letters with appropriate digits.

Answer 1

I think the digit will be 1 and 0 at the place of digit 1 there can be another digit

Answer 2

Given 1MN = MN

If 1MN is divisible by 3 then sum of

all the digits is divisible by 3

=> 1 + M + N = 3 × { 1 , 2 , 3 }

Let 1 + M + N = 3 × 2 = 6

M + N = 5 ------( 1 )

1MN/3 = MN

=> 1MN = 3( MN )

=> 1×100+M×10+N×1 = 3[M×10+N×1]

=> 100+10M+N= 3[10M+N ]

=> 100 + 10M + N = 30M + 3N

=> 100 = 30M + 3N - 10M - N

=> 100 = 20M + 2N

Divide each term with 2 , we get

=> 50 = 10M + N

=> 10M + N = 50 ----( 2 )

Subtract ( 1 ) from ( 2 ), we get

9M = 45

=> M = 45/9 = 5

Substitute M = 5 in equation ( 1 ),

we get

M + N = 5

=> 5 + N = 5

=> N = 5 - 5 = 0

Therefore ,

M = 5 , N =0

1MN/3 = MN

150/3 = 50

••••