tens place digit is 4 more than unit place digit. the number formed by interchanging the digits is 36 less than original number. find how many such numbers exist
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Let the two digit number be xy,
However, in unit system - it is represented as 10x + y
Now, as per the question, it is 36 more than the number obtained by reversing the digit - so here we frame the sentence in Mathematical language →
(10x + y) = 36 + (10y + x) {10y + x is the reverse of the number} → Eq 1
Also, x - y = 4 → Eq 2
Now solving the above 2 equations →
x - y = 4
i.e x > y, so x can be 5, 6, 7, 8, 9 and y can be 1, 2, 3, 4, 5 respectively.
So, two digit number can be 51, 62, 73, 84, 95
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