1.

sum of the digit of a two digit number is 11 the given number is less than the number obtained by interchanging the digits by 9 find the number

Answer»

Let the tens place digit be a

And Unit place digit be b

According to first condition,

a + b = 11 --------(1)

According to second condition

( 10a + b) - (10B +a) = 9

=> 10a + b - 10b - a = 9

=> 9a - 9b = 9

=> a - b = 1 ------(2)

On ADDING equation 1 and 2, we get

2a = 12

=> a = 6

Now,

On Substituting the value a in equation 1, we get

6 + b = 11

=> b = 5

Required number = 10 × 6 + 5

= 65


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