Consider all two digit numbers such that
Find the sum of all such two digit numbers.
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Let the one's digit be Y and ten's digit be X .
●According to first statement.
X > Y .
●According to second statement.
X + Y = 2 ( X − Y )
X − 3 Y = 0
X = 3 Y .
This statement gives that ten's digit should be 3 times the one's digit.
Now, putting Y as 1,2,3 but if you put Y greater than or equal to 4 the number will be of three digit or more.
X = 3 × 1 = 3
X = 3 × 2 = 6
X = 3 × 3 = 9 .
Now possible two digit numbers which satisfies both conditions are 3 1 , 6 2 , 9 3 .
Now, their sum becomes
3 1 + 6 2 + 9 3 = 1 8 6 .