1.

a two digit number is 3 more than 4 times the sum of its digits if 18 is added to the number the digits are reversed find the number

Answer»

Let the ones place digit be a

And UNIT place digit be B

According to first condition,

10a + b = 4 ( a+ b) + 3

=> 10a + b = 4a + 4b + 3

=> 10a - 4a + b - 4b = 3

=> 6a - 3b = 3

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

According to second condition,

10a +b + 18 = 10b + a

=> 10a + b - 10b - a = - 18

=> 9a - 9b = - 18

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

On SUBTRACTING EQUATION 2 from 1, we get

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

=> a = 3

On Substituting the value of a in equation (2), we get

3 - b = - 2

=> b = 5

Required number = 10a + b

= 10 × 3 + 5

= 30 + 5

= 35


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